I've just brought mine back from not running since 2004. Some direction....
1- I too, seriously doubt your transmission has anything to do with your problem. Or your thermostat.
2- the car has been sitting for 15 years, you are going to have a lot of reoccurring problems if you just started it up and didn't address the fuel system properly beforehand. Hopefully you got the old gas out. If you didn't, then my guess is that's your problem. Change your fuel filter. Blow out the lines. In my case, 4 out of the 6 injectors were bad, that might be a problem, too. Also in my case, the gas tank was powder coated and so was pristine inside, my fuel pump was fine but the insulating sleeve around it had disintegrated leaving junk in the bottom. I'd never start a car sitting for a long time without dropping the tank first.
3- A wise person once told me don't throw parts at it, it will just make you broke and mad. Do some diagnostics. An engine needs fuel, air, spark and compression. Start with one and don't proceed until you're sure you have the variable you're testing for.
4- Although my dash is different, it also didn't work and you're just dead in the water without it in these cars. I sent mine to Cluster Fix and he did a top notch job. I don't know if he does the computer screen on your car, but you might try calling him and ask. I'd also check the ground behind the battery and clean it. May bring it back to life.
Hope I've given you some direction.
-derdachshund