Listen closely! I had the exact same issue you were having. I spent lots of money trying to resolve this issue, including a new fuel pump and a new Engine Control Module ( the computer ). I decided to check my voltages at the relay terminal under the hood, for the fuel pump. Voltages were fine. Factory replacement fuel pump relay ( AC Delco ) didn't work. However, I could jump the terminals with a piece of wire, and force the pump to turn on. Here is what you do.
Go to AutoZone and buy a replacement relay for the fuel pump. Do not buy AC Delco brand relays! Oddly enough, the AutoZone relay worked, and the AC Delco relay did not, even though I tested the AC Delco relay using a multimeter, and checked good.
Go to AutoZone, spend the $15 bucks for THEIR brand of relay. Try the $15 dollar solution before you go replacing fuel pumps, ecm's, and crank sensors. Good luck!
Tuesday, August 14th, 2012 AT 3:26 AM