I have a 1996 eighty eight 3.8 at first the car

Could be crankshaft sensor,fuel filter,tune up coils and module.

Hi...it sounds like your fuel pump might be going...if you can, get a fuel pressure test done.
Let me know if I can help further,
over4dy

replace fuel pump You should have 48-55 psi with key on engine off, if not within specs replace pump.

YOUR ALTERNATOR IS PROBABLY THE PROBLEM.

Fuel pressure for the 3.3L engine should be about 34 - 36 psi. Pressure for the 3.8L is about 40 - 47 psi.

one of the common causes of this is a defective electric fuel pump.

How did you determine that the voltage is OK? Will it run the headlights, brakelights, and horn at the same time? It could have enough voltage without enough amperage(power). It could be a loose cable - that is what I would check first.

If it is getting fuel (with good fuel pressure) and spark (blue), then your problem is either timing related which could come from a snapped timing belt, or compression related which could be due to a blown head gasket. In which case you would replace the timing belt or replace the head gasket respectively.

Check fuses

You may have a faulty crank sensor again. Next time it cuts off hot, spray or pour water on it and then try to see if it will crank. These cars had a cutting off problem with ecm #1228253 but most of them would start right back up. If it has that number on it replace it.with #16198264 or newer number. Get a delco and not an aftermarket ecm..