I did this entire job not long ago. I replaced the in-tank fuel sender unit (the assembly, pump, sock filter - everything). Car refused to start at all - before it just sputtered on low gas making turns. I killed the car after doing only this.

I bought an AutoZone main pump and new filter - still no start. I checked all of my ground wires (both main pump and in-tank pump) and I got a start - then it died.

The clear fact was that at the fuel rail on the engine, I was not getting fuel.

Long story short - I went to junk yard, pulled OEM main pump from a car, bench tested it to make sure it worked. I went home, installed it - VRROOOOOOM! Perfect start.

Also, couple things. Make sure:
1- Fuel pump relay is good
2- Fuel pump fuse is not blown
3- Wires on pump are connected well
Trick: Turn your key enough to 'bump' the engine - don't crank it. Turn it all the way off. Each bump primes the fuel pump. After about 5 or 6 of these, your car should fire up without as much as 2 or 3 revs. This saves lots of cranking and battery power and forces fuel from the pump to the injectors.

Last - you don't need any tool to remove the plastic ring on the fuel tank for the sender unit. A hammer (rubber if you have it) and flat blade screw driver is all you need to tap it loose. Avoid doing this job if you can, it is a pain in the butt the first time.