Car wont start after shut off

Ok i bought of a friend of mine a 96 cutlass 3.1 for 500 bucks cause he had it for 3 years and wanted a new car and he did not know what is wrong with it.

After you sut the car off and you wait more then 20 mins the car will start but will stall after that its like it is hick-up.

I checked the fpr and just a little air came from it.
We put a new fuelk filter on it the old 1 was like 2 pounds really and now there is no fuel coming from the pump fuel that is b4 the filter is the fuel pump bad the fuse is good and the relay.
Plus the car does not get hot.

What is your fuel pressure if any? If there is no fuel coming from pump then more than likely it is bad. Either that or the wiring to the pump is bad/damaged. Also if the old fuel filter was clogged badly, then may want to check fuel lines or fuel pump filter for clogs/buildup.