Why does my car idle perfectly but hesitate/die immediately after applying throttle?
I have a 88 Ford Thunderbird Turbo Coupe in perfect garage kept condition. It was stored for 15 years, brought it back to life and now six months later I can't figure out what the hell the problem is. It happened going down the road all of a sudden the car would not go, RPMs slowly went down and then I was stuck. I replaced the fuel pump again, and the car will idle perfectly, but the moment you touch the throttle the car will jerk and die. Oddly enough if I rev and feather into the higher RPMs I can put it in 1st and take off like a bat out of hell. Driving the car down the road this way I have no problems unless I give it gas too quickly, then she will start jerking like a wild bull bucking down the street. I'm starting to lose hope for the car because I've replaced so many parts. I borrowed a buddies code reader, but on system checking it would rev the car up and just immediately die, so I could never pull codes. On the engine off test I got a 26 and I replaced the MAF, but still no luck.
Parts replaced
Fuel Pump (twice, the first pump was 15 years old, it was new, but was never installed)
Rotor and Button
Spark Plugs
Spark Plug Wires
Battery
Fuel Filter
TPS
Fuel Pressure Regulator
Mass Air Flow
I tried checking for any vacuum leaks, I sprayed starter fluid all in the engine bay, I couldn't get any rpm changes at idle. 
If it was an engine with a carburettor, that could indicate the throttle pump was not working; but with the sensors you list it's a fuel injected engine.
The obvious thing are:
A fuel flow restriction of some sort.
The turbo is seized and restricting gasflow rather than boosting it?
The turbo control mechanism is not working or seized up - there could be a pressure, vacuum or electric actuator on it that is not working properly.
I'd expect the turbo control system to actuate in some way changing from idle to acceleration; if you blip the throttle and nothing happens on the turbo mechanism, it gives you somewhere to look.
Cutting out as you describe could be too little fuel or too little air; it's difficult to say without seeing the vehicle.
I would also flush the entire fuel system on principle with a vehicle that has been standing that long - it could have particles of rust or bits of peeling paint just about anywhere through it, from the tank to the injectors…
It's probably worth joining one of the Ford enthusiast forums where you can ask people with specific knowledge of that exact engine & fuel / turbo system.
I'm fairly familiar with general Ford engines of that era but I've never seen the turbo version.
Edit - Apparently there are two versions of the injection system, with a changeover around 1988. The later one [with a MAF sensor] uses timed sequential injection rather than bulk injection and relies on a cam position sensor.
It appears a malfunction in the cam sensor could be responsible for the type of symptoms you describe?
Get a smoke machine and check for vacuum leaks. Get a fuel pressure gauge and check fuel pressure. Check for a leaking fuel pressure regulator.
Nice Thunderbird.
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