1982 928 US only runs with fuel pump off

Vehicle had been stored for ten years when I got it. I had fuel tank cleaned, replaced fuel filter, fuel pump, all fuel lines at tank area. I have jumped the fuel pump at the relay so can remotely operate it. I can get the car to start and run, not great but OK, with the fuel pump off. As soon as the pump is turned on, the car stops. I have replaced all vacuum lines and spark plugs. Have cleaned and verified proper operation of all fuel injectors, including the cold start injector. Not sure where to go next.

You didn't mention how long the engine runs with the fuel pump off ... it can't be very long because the fuel pressure will quickly fall.  What is likely happening is the engine is flooding and running without the fuel pump just sucks the remaining fuel from the intake and as the mixture leans out a bit it briefly runs until the fumes are all consumed.  My guess is the fuel pressure regulator/dampers and/or fuel injectors are leaking.  All should be removed and inspected.