Where is the fuel pump located on a 2005 chevy cobalt?

There isn't one.
What testing have you done?
Make sure battery has a full charge. If it cranks good but won't start, have a helper crank it while you visually check for spark at the plugs. If spark everywhere, use a gage and check proper fuel pressure and fuel injector pulse. If your missing everything check for rpm signal. Any applicable trouble codes?
When you first turn on the key, no crank, can you hear the fuel pump run for a couple seconds? There is a fuel pump fuse in underhood fuse box.

No sensor that I know of that would affect pump operation.
Have you checked the pump relay ?

Fuel pump , fuel pump relay , Test fuel system . GM Fuel Pump Relay Testing

You have no voltage at 15 amp fuel pump fuse in the under hood fuse/relay center ? There is a fuel pump relay also in same under hood fuse box. The fuel pump fuse gets power from the fuel pump relay. The ( PCM ) engine computer controls that relay, gives power or ground electronically to turn the relay on giving power to the fuel pump through the fuel pump fuse. You could have a bad relay or an anti-theft system problem . What engine does you vehicle have 2.0 L or 2.2 L the 2.0 L engine gets power differently to fuel pump .

If you do not have the fuse box picture in your car book (in the glove box), google 'location for fuel pump fuse on 2006 Chevy Cobalt'. You will get all the information necessary to find the fuse.

drain your tank first. then drop it easier doing that to replace the pump.

Try following the fuel lines from the pump and look for a squashed steel line that is blocking the fuel flow. IT is possible the some wires were damaged from the debris.

if im correct there should be a red wire on the drivers side of the firewall not connected to anything. take a jumper wire to the positive side of the batt. and connect it to the red wire. if you can hear the fuel pump, there is a short somewhere. it could be as simple as the inertia switch or emergency shut-off switch. check the fuel pump relay too

The 2005 Cobalt is fuel injected. It does not have a carburetor. If you are looking for the fuel injector it will depend on if it is thorottle body injected or direct port injection. Typically they are throttle body fed cars. Follow the air cleaner box up and the aluminum .housing will have the fuel injector in in.

if you are used to hearing the fuel pump but cannpt hear it anymore, it's probably a fuse or the pump. Pump replacement is expensive, so always make sure the pump is getting voltage before replacing.