[jsgold]

Sounds like a familar problem with most GMs. The TCC solenoid goes bad or gets clogged and when it gets hot it causes the transmission to act up. The car shakes and shudders and acts like a standard shift car in high gear going slow. Stalls out. Car starts fine but will stall as soon as shifted into ANY gear. When it cools down a bit it will work again for a while. This locks the torque converter and when it goes bad it won't release. Usually hard to fix on Lumina/Corsica due to location. A cheap part (<$30) but can cost 150-250 to replace, as most transmission shops insist on a total flush of the system to keep the new one from clogging. You can unhook the TCC and it will work OK, except, you will have lower mpg. Not a lot though. Most people unhook them and forget them. Up to you. Assuming yours is a 3.1 it should be under your air filter housing. Remove the filter, cover, and then the housing. Look underneath for a 4 pin connector. Unplug it and try it out. If it works OK you are done, unless you choose to fix it later. On some cars this won't help, such as 4 speed transmissions on Buicks etc., but should do the trick on yours.
If these symptoms are not same as yours you could have other problems, but, most of the ones I can think of occur whether in gear or not.