You DO realize that the fuel pump only gets power for a second or two by a timer when the key is turned on, but engine is not started?
To test this, be looking at your voltmeter / testlight while someone else turns on the key. If you get power and it quickly shuts off, you're good.
Your problem is probably the pump itself or the connection. The way that connector is designed, it's very easy to plug it in and have one of the prongs shoved up in the rubber plug, along side the actual metal socket, instead of IN it. This will work for a little while, but not for long... I know from experience!