Pretty UNcommon for one of our pumps to go out or bad. Only time I have seen one on its way out was from the owner not changing the oil and filter like they should, and the front aluminum cover, which the pump rides in, was pretty destroyed.
My oil pressure reads 50 on the dot on a cold start, and will go down to around 20/25 when its warm and I'm not on the throttle.
Not all after market sending units are the same. Last one I had read 60 no matter what, warm...cold...at idle, driving down the high way. It was leaking, so replaced it, now this one makes the gauge move.
You have oil pressure at start up...so your pump is pumping...
I believe your problem lies in either not having enough oil in your motor, or your sending unit its self for your gauge. You said your oil light came on...so you have your stock sender still plumbed in?
~F~