I JUST GOT A NEW FUEL PUMP PUT IN MY 2003 3.8 LITER IMPALA, AN THE FUEL PUMP ISN'T GETTING THE SIGNAL TO TURN ON

Chevy doesn't have a inertia switch . If the engine dies after a wreck the fuel pump shuts off because the PCM doesn't see a crankshaft position sensor signal . The engine has to be running or cranking . GM Fuel Pump Relay Testing YouTube

I sounds like you have a fuel flow problem. Replace the in-line fuel filer located in the fuel line in front of the rear tire. Check out this web site for "how to" replace the in-line fuel filter.
http://www.ehow.com/how_6724057_install-filter-2003-chevy-impala.html

take them out stick them in some seaform for 24 hours put them back on the fual rail but not in the intake turn the key and see if they spray if they dont trashs them buy new they are cheap

Either the pump relay is not working right, or the check valve in the pump is letting fuel drain back into the tank when you turn the engine off.
You would check the pump relay to see if it is getting a ground signal from the computer when you first turn the key on, then look at base fuel pressure with a gauge if necessary.

firstly remove the fuel pump from the tank and test it by connecting the leads from the pump to a 12 volt battery....if the pump turns on then test the wires running from the pump to the front of vehicle.....since you have replaced the relay then that is not the issue also some vehicles have two sets of fuse blocks instead of the standard one ......does the pump spin up at all when you turn your key to the first position without starting the engine? if it does then you need to test the fuel pressure getting to the intake....i replaced a pump recently that was only pushing 8psi to the engine instead of the needed 52-66psi new pump fixed the whole issue

You need to have the correct pressure, Key on engine off the fuel pressure should be at 55psi to 62psi.Also inorder for the fuel pump to turn on the cranksensor must beable to produce the proper signal for the fuel pump to turn on,

sounds like your sending unit is bad. unfortunately the sending unit is probably with the fuel pump in the gas tank.

This tutorial will help you : http://www.ehow.com/how_4508670_replace-water-pump-chevy-impala.html

you will need to pull steering wheel you have a clock spring for the air bag behind it dangerous for a on trained technician simply put the air bag could kill you

we had the same problem with our 2003 impala...took it to the shop and was told it was the hazard lights.