1994 Oldsmobile 88 car dying

The car will start up normally with everything running fine but after driven a few places it will die and stay dead for an hour or two and then run fine again. It usually dies at low speed or idling. it will start "choking" at higher speed like on the highway but if I feep it going by pumping the gas pedal it will pull through and then start running again properly. Idling or at low speed it will cut off and this usually coincides with using the power windows or when I open the door and the inside lights come on. There is some sort of security device on the car but I bought used so Im not sure how that is supposse to work but on the the dash there is a lighted word security that lights up next to the gauges and other dash info and this light seems to go off and on randomly. It a great car but I cant use it because I do not know where i
I'll get stuck. The fuel pump has been replaced but 2 mechanics have not been able to pin this down.

Thank You
David in Petersburg Va