2000 Chevy Impala fuel pump runs when key turned to ACC

Hi I have a 2000 chevy Impala which when I got it, it wasn't getting power to starter when key turned to start.
Finally corrected that with new Ignition Cylinder (I did the switch also.)The message center continuely shows battery then low fuel, then security in message box. Radio won't play when car is running.I turn the key from Off to ACC and I hear the fuek pump run with out going to the "On" position. The car starts, now, but something else is mess-up. The fuel tank is full as far as I can tell, because I poured gas in and it over flowed out the filler tube, so is there suppose to be power to the fuel pump when the key is turned to ACC?
Thanks any help will b greatly appreciated.
Ron M