I did some checking and I think I know what's going on with our beater. (Cavalier). Please confirm that this blue plug on the tranny is for the torque converter clutch solenoid. If unplugged, it stops the torque converter from locking up. After a short test drive, I think I found that it won't lock up with it unplugged, but it does lock up with it plugged in. My problem is when you're in drive and you come to a stop, sometimes it wants to die and pings, jerks, etc when you go to take off again. Usuaully dies though under all the stress.

Please let me know if you're sure this is the plug for that soleniod. You're looking at the tranny from the front of the car, and this plug faces the radiator. Again, 1995 Cavalier.

 

I dunno whether you have the 3 speed or 4 speed auto, but here's pictures of both:
3 speed 3T40

4 speed 4T40-E

TCC solenoids are common failure items on GM transaxles. The solenoid sticks and keeps the converter locked up, so when you come to stop and go to take off, it's as if you were starting out in high gear with a manual transmission. I think your pictures show the TCC connector, but I'm not sure; no spricken ze GM.

 

This looks kinda like your Cavalier:

Near 13 is where it looks like the connector for the TCC comes through the case. I know there's some GM guys floating around here somewhere, can anyone else verify?