Well it would seem that there is some sort of electrical problem. Perhaps the ground wires are bad, or there is something related to the Fuel Pump (like the wires that connect to the fuel pump may be bad?) Maybe your Ignition Coil/Wires are starting to go bad, or your spark plugs?
I think it would be good to check a lot of those things out. Though I am not an expert on this problem, just throwing out some possibilities. Good luck with your problem, I hope you find it