Today I clunked my car from school to the mechanic's garage near my house (about 20 mile drive, and a scary one at that). The car was accelerating all by itself for the most part. I exited my parking space, left the lot, drove around the side and through the front of the campus, and went out onto the main road without touching my gas pedal once. The car would gargle and yank like a dog on a leash whenever I would stop. Plus I had all the fun with driving at insane RPMs because the transmission wouldn't shift gears due to not getting accurate throttle readings.
I got to the garage without dying and left the car with them for the afternoon to have them test various sensors, the engine control module, run advanced diagnostics, and drive the car. A little over two hours after I dropped it off, they called me and told me they had finished. My throttle position sensor that I bought on Sunday is garbage so I'm returning it. The owner had a black Pontiac Grand Prix with the same 3800 engine that I have so he let me have the TPS from it. They didn't find anything pinpointing the refusal to idle with a hot engine however. The best bet that they gave me was to fully remove the entire throttle body and scrub it out, focusing on the throttle plate to make sure there isn't gunk on it blocking air flow. My dad and I pulled the air intake off recently as well as the connected sensors to clean it up some, but we didn't go that far with it. They also immediately noticed how much my engine shakes due to the poor front engine mount and suggested I move that up on my to-do list. Although farfetched, they said there's a faint possibility that the wobbling engine could be pulling or compressing some wires and the car's electrical system shuts off the engine to prevent damage. That wouldn't explain how my engine starts flawlessly while cold though.
They tried charging me $200 just for checking the electrical system(s) and driving the car around to give me ideas. I managed to whittle them down to $150 and [quite shrewdly] had them walk me through every single problem I've ever had with the car since I got it. They put it up on the lift so I could check out the brake lines (holy crap my left rear line though) and gave me estimates for repairs ($200 for just rear, $350 for all). I had them look at my terribly rusted catalytic converter, which apparently isn't a problem until time comes to replace it (it's so bad that it will need to be chopped off). The popping noise by my left front end could be from some unneeded movement where the wheel connects to the suspension, but nothing stood out so I'm not worried about it. My fuel pump (I already have a new replacement) is so rusty that I can't take it off normally but I should still be able to do it from home.