I can't make any headway in the Silver races. Is there something I'm just not getting? Is it the fact that a trackball mouse is woefully inadequate? Am I just old?

Have you upgraded your car or bought a better one ?

I'm on the same boat due to a minor (major) mistake. I bought a better car (speed devil) and gave it used tires, spending almost all of my money in a couple of speed upgrades. Now my car is a freaking ballerina, liking to shake it's backside on every curve and spinning around whenever I go off track and try to get back on the road. If I slow down to avoid crashing into cranes or trees, the other cars fly past me.
I can't sell any part from my newly upgraded car, so I have to win some more money in order to buy regular tires to improve the handling but winning something with a dancing car is quite difficult.

Personally, I find the heavier the car the better. More weight gives you more traction, so you can take corners faster. Also, other cars can't push you around as much if you drive a big tank of a car.
For money problems, though it's a bit grindy, you can do the special events (long jump, high jump, etc.) to win some extra cash. Handling isn't as important as speed for those. Also, see above: you may want to eventually consider a car with more weight and less speed. The farther you get, the curvier the tracks are.

I bought the heaviest car possible in Bronze, and have been upgrading consistently since then -- mostly tires and engine. Haven't tried any of the specials yet -- that's a great idea, thanks!

I'm also stuck in silver, to the point where I used a save mod to see if it was just me using my money badly. It wasn't. A combination of problems lead up to getting stuck:
1) The CPU players are faster, so you need a faster car to catch them on the straights
2) The faster cars you can buy, even the heavest, handle terribly and spin at a moments notice and going slow gives you problem 1) again
3) Even tapping a single thing with a faster car seems to rag-doll you in a second. Even at 30mph I've popped out of the windscreen and flown about a million yards.
4) If you have to RESET, you end up a way back and dead still. The amount of times Ive then been rear-ended and span out... again... into a tree. *pop* I go again.
5) The CPU drivers really don't have the handling issues you do, they stick to the track like glue.
Its a shame you have to drive carefully, it seems to punish you for crashing really, when it seems a major point of the game. I've beat only one Silver track, and I'm not kidding when I say my back windscreen was still intact when I finished - that's how well and carefully I had to drive to win (after a million attempts)

This, plus the fact that you're better off restarting a race than using reset were my main complaints with the game.
If you like the idea, but not the execution, I recommend FlatOut 2:
- Ragdolling is much harder to do. Perhaps too much so.
- Resetting is a rolling start, and you're given a few seconds of intangibility.
- Cars can be test-driven, so you can see how fast they are and how they handle on various surfaces
- Nitro is awarded for air-time, and every track has some kind of ramp / drop, so if you need a boost, you don't have to worry about finding something or someone to smash.
- You're awarded both nitro and cash for hitting opponents. The harder, the better. There are also cash awards to the drivers that cause the most damage overall, both to scenery and other cars.

I'm also starting to call it quits on the game. I love playing the bonus tracks though and sometimes I just prefer to ride bronze. I'm pretty sure I won't be able to finish this game.
Couple of things I'm hating:
1) Taking a curve wrong, ending up almost perpendicular to the road, so another car crashes on me and turns me around so if i drive I end up going in the wrong direction and getting the car to turn around without overturning is a pain.
2) Getting stuck on tires, with your wheels spinning and unable to pull out. It's so easy to do and it usually happens to me in the last lap.

I had no problems on Silver... used Fasthammer for both Silver and Gold challenges with no major problems. What car have you been using?

Speed devil. Fast but unhandly, specially if you give it more upgrades for speed. I've already reached the top of the tires and suspension handling.

Same car I've been using, and it handles like an elephant with roller-skates on ice.

You should try switching to Fasthammer. Even without upgrades, it has great handling, better than most other cars. With upgrades, it can definitely compete with the Gold level cars easily in most tracks. Highly recommended.

Cheers, I'll give it a go when I mange to set up my main machine.

Where do you find these cars? I only see Pepper, Grinder, Blocker, Blockhead, Bullet. Do you unlock more somewhere?

Yes. The cars you list are all bronze level. When you complete bronze, more cars are unlocked, and more yet again when you complete silver.