I don't see how you thought it was the pump or the module in the pump. Take a look at what is below. We know the BCM and CLP/SSM are working from your post above.
But the door lock and key FOB operate thru the SKREEM. The button on the console is wired to the BCM, the door ajar wiring goes to the CLP/SSM.
I vote "Bad SKREEM". Keep in mind there are TWO halves of the SKREEM, the 1/2 that is powered up all the time to operate door locks (is that fuse blown?) and the other half that powers up with the key to initiate the FOB reading and start sequence. NO ONE can say for sure, and I seldom disagree with Josh or Rob -but I vote "bad skreem".