It starts but will not stay running

SOURCE: starts then dies

check your fuel pump relay 

SOURCE: fuel pump stays running after car is turned off. battery stays dead have to get jumped to start car.

The only way the pump will run is if it has a live 12v dc supply to one side and an earth return to the other.

Most cars have the earth side of the pump grounded down to the chassis so I would go for the fact that you have a short on the loom or a faulty ignition barrel.

An auto electrician would isolate the pump wiring to see where the feed was coming from then repair the fault

SOURCE: fuel pump

usually in the top of the fuel tank where the sender unit is look in the trunk for the wire & the plate [cover]

SOURCE: without any prior problems my

Have you checked the distributor or coils? Maybe your rotor is not turning. It could be so many things.

SOURCE: 1989 buick century 3.3 car starts idles but wont run when giving gas it acts like running out of fuel but fuel pump stay running and has pressure new fuel filter spray carb cleaner it will stay runnin

have you put a fuel pressure gauge on it if so how many ponds of pressure does it have also if this is a distributerless car turn engine with a socket see if there is slack in rotation if you turn counter clockwise 1/4 turn stop and turn clockwise if so you more than likely have a stretched timing chain or jumped time