Possible fuel pump relay gone/going or the controller

You know when you put the car into on and the power lights comes on and you can hear the fuel pump prime? Does that fine for the first start, then if I say run into the shop for a couple of minutes and come back out, turn to on and power light will illuminate but I don't hear the fuel pump, can't start the car, will turn over but yeah, if I give it some gas sometimes it will start on me but then stall.. Very annoying