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The pump only should run if the engine is cranking or running. The ecu only turns the relay on after it see's that the engine is turning!

The main large pump and tank pump will continue to run for a couple seconds after cranking if you listen carefully.

If it is hard to hear the large outside pump it then I would suspect the check valve on the outlet of the pump. The fuel rail needs 35psi to make the injectors spray and hold 10 psi after cranking for approx. ten minutes. Bad check valves cause hard starting or a no run condition and cost about $14 from Volvo the last time I bought one. A bad pressure regulator can also leak off pressure but fail less often has been my experience. Need to check for rest pressure on the rail or at least fuel held there after cranking. If you disconnect the return to the tank from the fuel pressure regulator you should not see fuel leak fron the valve until vac. is applied.

If you are sure that the power is not getting to the pump wire you may want to check under the rear seat on the drivers side. There is a connector under the carpet that may hve been damaged. It feeds the main fuel pump at the same time. An open circuit is what you describe. A short woud blow a fuse.

I think when you have power with key on you are getting the power from the fuel tank gauge. If you had a volt meter you would see a pulsing voltage and is current limited by a instrument cluster regulator board on the back of the instrument panel. I hope you haven't pulled to much current through it or your gauges won't work or be accurate!