I can definitely relate to the love of your WRT54G. I have the WRTSL54GS from the same family with a little more features on it. They made several different hardware versions of the WRT54G and some did suck but all the Linux compatible ones will go down in geek history as one of the best consumer networking products of it's time.
In case you aren't ready to give up on that trusty workhorse yet, I've rarely if ever seen those actually break. The most common failure on them is the AC to DC converter power brick. As those bricks age, their output voltages/current can stray from their originally designed tolerance. In this case you would see similar behavior as you're describing (actually works but can start to act flakey here and there.) You could try another brick. Those bricks list their output current and voltage so a universal type one that meets those specs should work. This might be all you need and you get off spending probably less than 20 bucks.

Since you mentioned you were just recently aware of the web based interface of routers, here is a tip to help simplify the process of getting into them that works on any NT based OS.
- type "cmd /k ipconfig /all" without the quotes in the search field in start menu and hit enter.
( see pic)

- this brings up your network adapters info. The IP address listed as the "Default Gateway" is always the router's ip address you type in your browser to access the web interface. This will work on any router.

- Normally in a default out-of-the-box config, account name is always admin and the password either blank or admin also.

If not, the default password can usually be found on routerpasswords.com.

It's not a power failure. The lights have never gone out on this thing. It's just random (as in "frequent but with no real pattern", not as in "scattered") lockups an even bad data transfer. And that's just the wired (Modem to router to PC) connection.