I picked up an 89 Rx7 GTU w/automatic trans and after doing an engine rebuild, when you put it in gear, it bows up like it wants to move and dies. Put it up on jackstands and it will go in gear and run, but shakes like crazy.
Changing to manaul is out of the question. Person I bought for can't drive manual.
Here is how the car is:

The car sat for 3-5 years. Bad engine.
Fresh rebuilt engine.
header no cats.
6 port actuators don't work. Port sleeves are closed and actuators and actuator rods have been removed. So much carbon in the sleeves and actuator rods, 1 rod broke. Couldn't get the rods to loosen up. LIM was welded up where actuator rods were. All vacuum lines capped or rehooked up.
Air pump blocked off.
Rtek computer w/eomp delete.
Haven't changed tranny fluids,filter or modulator valve yet.

I don't know the maintenance history on the car, but probably pretty bad. The engine had more carbon in it than any engine I've ever seen. My friend that built the engine(Drama) said in all his years, he had never seen anything like it. Tranny fliud/filter may be original for all I know.
Talked to a mechanic friend and he says it sounds like the clutch packs are frozen.
What about bad driveshaft?
Flat spotted tires from sitting? We pulled the car to his house(about 1 mile), he said they were but got better as we went.
These would explain vibration but not dying.

Sorry so long, any help is greatly appreciated. Hope I covered it all.

 

You rebuilt the engine correct?
Did you check the drive train to see if it actually was operational?.
Brakes will seize up if it sits too long.If anything is hindering the engine from putting power to the wheels then Yes,it will Fall on it's face and die.
Think of it like if you were in a race and someone tied to the the starting line.NO go.