1997 Ford Mustang stalls and sometimes does not start

1997 Ford Mustang I was driving my car and it started to cut out here and there. It would stall out sometimes or just not start other times; I could here that the fuel pump was not on when the car was dying or not starting. It finally died and had to be towed home. After I got home the car started right up. Then it was dead again later on that night. I dropped the tank and changed the connection where the wires plug to the fuel pump on the cap because they were in pretty bad shape. After that, the car started right up and drove around for a while and it ran great. After I got home I went to go back out and it was dead again so I did not fix anything there. It seemed to me that my fuel pump was on its way out so I changed it. That did nothing. I tested the old pump and both are working fine. I changed the fuel pump relay under the seat and that was not it either. I tested the wires with a meter, I had the car hooked up with jumper cables and I was getting 10.8 to 11 volts at the cap of the tank. I was also getting the same out of the relay. I am getting 13.5 volts from the battery when hooked up to the jumper cables, and I was getting 13.5 out of the inertia switch in the trunk, the power was going through the switch so I think it is fine. What else could be the problem? The 11 volts at the tank would not even light a test lamp (I figured it shouldat least light that) but no. I am having no luck and am not sure what to do. I tried grounding the ground wire coming out of the pump to the frame and that did nothing so I assume the ground is okay. Any help would be greatly appreciated!