I'm imprisoned in the military base by the big mutants. If I lockpick the door, I'm seen no matter what. He kills me on sight, or he takes me to the leader again, who then kills me on sight. What the hell do I do now!?

This has never happened to me in a game, but I think what you have to do is spend all your APs running away. If you enter combat mode before he takes his first shot, maybe you can get around a corner in time (I've never seen the map). There's no point in looking for your lost stuff, it apparently isn't to be found.
If you can manage to get away, I think it is possible to sneak around or run away from all combat. There is a way to set off a self destruct sequence. There are also guys in purple robes. I think you could steal the robes and wear them to make it easier to get past guards when running away from the base.

I hate to be a pessimist, but your best bet is probably reloading to an earlier save. Outside of that, all you can really do is run away or kill some mutants bare handed to get a weapon.

use falche, take 'em all out with your fists of fury.
j/k reload.

Your stuff should be in the locker towards the top of the level.

You guys don't seem to understand. I take one single step outside my door and I'm dead. There are no other options! I can't believe I'm the only person to stumble on this. None of the FAQs mention this. I'm not reloading an earlier save. Any game that makes you do such a thing is a poorly design game.

hmmm, that is strange. try waiting a while to see if the guard walks away from the door. the same thing happened to me the first time i played (being captured in necropolis by the super mutants and taken to the military base).
if you're able to get out of our cell, then you only have a few options. i hope that you have moderately-high big guns, science, repair, and speech skills.
you can lockpick the other cells, i can't remember if there is anything in any of them, though. there's a woman you can talk to, but she isn't any help. one thing you can do is take the elevator across the hall from your cell and go down to level 4. when at level 4, there's a room directly south of the elevator. there are some super mutants in there. if your speech skills are up to par, you can convince them that the master has given you a super-secret mission, and they will leave you alone. there's a footlocker with some explosives, which might come in handy.
more importantly, there's a mr. handy. go up to mr. handy -- this is where your science and repair skills will be useful. repair mr. handy, and then use science to get the robot functioning again. tell mr. handy to resume its programmed function. mr. handy will move out of the room and down the hall towards another force field. it'll malfunction and blow up against the force field, knocking the field down in the process. mr. handy will also drop a minigun. you'll need that.
go through the destroyed force field and you'll find a computer room with a bunch of robed cathedral guys. you can kill them all if you want, but i don't remember if its necessary to access the computer. they also have weapons on them (as well as the robes, which is at least a bit of armor. unfortunately, once you open fire on them, the base alarm goes off, so sneaking around in a robe won't work.)
there's a computer in the room you'll need to use science on. the computer will give you a bunch of codes -- all of them set the self-destruct mechanism. the one second from the last sets it silently for 3 minutes. you can now try to escape, but that won't be likely. you might be able to take out some super mutants with the mini gun, but it'll be incredibly difficult, since you have no items or armor. and you'll be faced with the problem of yellow force fields that you won't be able to lower (although, you could try using repair on the force fields. it worked in fallout 2. i never tried in fallout 1).
all you can most likely do from here is blow up with the base. you still win... but you die at the same time. i hope this helps.

Don't blame the game.
You were the one who talked to one of the bad guys and got captured. You shouldn't be wandering the military base unless you're packing some serious heat - hardened power armor, turbo plasma rifle and laser gattling gun. You shouldn't need to talk to anyone - you should be capable of melting a room full of super mutants in a few rounds of combat!
If you keep getting shot, don't take one single step outside your door until you enter combat mode!
If you can open the door without getting shot at, you should move right to the edge of the doorway and then hit the "A" key on your keyboard to enter combat mode. It then becomes your turn, and the Mutant Guard can't start shooting at you until you run out of Action Points or click the "End Turn" button. I don't know the layout of the room you are in, but hopefully you can get around a corner before the end of your turn. If the Guard has to blow all his Action Points keeping up with you, he won't be able to fire his gun. I'm not sure how far he will chase you, but if you can make it to an elevator, I think you would be in the clear.
By the way, do they still hate you in Junktown? ;-)
When was the last time you saved before you got captured? You should have at least saved right at the beginning of entering the military base. If you forgot to save for several hours before you got to the military base, that's a problem for sure.

to be fair, if mozgus is where i think he is, then he was likely captured in necropolis after talking to harry, then taken to the military base. i doubt he tried walking in through the front door and then got captured -- there are at least three, if memory serves correct, super mutants guarding the door. they would have killed him before he even got inside.

I forgot that it is possible to be captured by the Necropolis super mutants. I don't think I ever talked to those guys. I didn't like the look of them so I started shooting them with my Sniper Rifle from across the street. Superior negotiations through superior firepower!
If you have a radio, you can trick three out of four of the super mutants guarding the base to leave.

oh yeah, i forgot about that. and you'll get 1500 XP, i believe. you can even do it after you've killed the outdoor guards and still get the XP.

Yeah but you are wrong. I did kill 3 of the mutants in front of the base, and let the 4th one talk to me. The possibility of being led inside and using my high speech skill to finish the mission for the brotherhood intrigued me. Everyone told me this game is sooooo limitless, and that you SHOULDN'T have to micro-manage saves. They ENCOURAGED me to simply trek on after every choice without worry. Clearly this game is not such.
As for the fanboys trying to defend such an obvious flaw, there's a very important rule of RPGs that you DO NOT BREAK. It's called the Point of No Return. The rule is that you do not allow saving past this point, unless it's the end section of the game, and even then, it's a stupid thing to do. If getting captured is a point of no return, then it should have a bad ending FMV right then and there.
This is a flaw in game design, and the developers should be given no sympathy for it. You do not punish your customer for paying for your game and spending 15 hours on it, by permanently halting their progress in it.
There should be a means of escape from any situation. You're supposed to be crafty! You're supposed to have free will in these games; the total opposite of Japanese RPGs. Why couldn't there be a vent duct to discover with my perception stat and escape by? Why couldn't there be means to convince the prisoner on the other side of the wall to cause a distraction (via your charisma stat) while you sneak past the guard's back after lockpicking the door? You see what I just did there? I'm a videogame developer already! Wow, this is easy!

ok, i see now. but did you try waiting for the guard to move? i've also noticed that reloading a save over and over can sometimes reposition characters in the game. i've been trapped in that cell before, and i have gotten out and run all around the base. i know it's possible.

Whow, calm down there dude. Before leaving the room, pick up the pistol and the stimpacks from the dead dude in your cell. You have one of two options; turn on stealth and go to the elevator and go directly to the room in the upper left hand corner and set the base to blow up with alarms in 5 minutes by using the computer ( I think this is the third choice; just save your game once your in the room with all the robed guys). That should cause the mutants to go into a hissy fit. The second option is to run like hell past the the guards (this is good if you have bonus move as a perk). If you fail at those two....just reload the game earlier and don't make the same mistake twice

There's nothing wrong with your approach, but even with a high speech skill, there's always the chance of failure. It's just like combat, in that even if you're armored up and carrying the BFG 9000, a lucky crit can still splatter you across the screen. When you tried to talk to the guy, and wound up getting captured, it's because you blew your speech check. It happens. Most players just re-load and try again.
Who told you not to save? If you listented to them, you took some bad advice. Even the official manual says to save often. Every hint or suggestion I've ever seen related to these games has said it is important to save often. If you're not making full use of the save function, then you're playing what's known as an "Ironman" game. If you signed yourself up for that kind of torture, when you get a bad result you're supposed to start over from the beginning with a smile on your face.
I still don't see where this is a flaw. The world of Fallout is dangerous. Sometimes you just die in combat. I got killed by the super mutants a few times in the military base before I made it all the way through. Even in power armor, a lucky hit with a rocket will take you out. You can also blow important skill checks or dialogue options. When you fail at something important you just re-load and try again.
The walkthroughs I have looked at all seem to imply that it is possible to escape from your situation. Your equipment is supposely in a guard room on the same floor as your cell, and if you have any NPCs, they should be hanging around with all of their stuff. I don't know your full situation and I've never been captured myself, so I can't tell you exactly what to do. But it's not impossible to escape, because other players have managed to do it.