The fuel pump relay has the pump pressurize the system to enable the engine to start then cuts the pump until it gets a signal that the engine is running. So likely that something's wrong with the relay or the signal.

Does the tach register when you're cranking?

I think an 86 300E has a separate fuel pump relay. Some cars have the relay feature built in to the ECU or something like that.

Sixto
95 S420
87 300SDL