On mazda mpv 2001, when you turn the key to the on position, should the fuel pump prime? should you hear the fuel pump run?

Check or replace the relay for the fuel pump.

I would suspect that the fuel pump is no good. Running an electric fuel pump on empty tank is inviting problems.
Sometimes if a vehicle runs out of fuel it can get air in the fuel lines. Any time a vehicle runs out of fuel and more fuel is added, the key should be turned to the 'On' position then back to the 'Off' position three or four times to prime the fuel pump. Priming the fuel pump will remove any air that may have gotten into the lines as a result of the vehicle running out of fuel.
If priming the fuel pump does not start the vehicle, I would recommend having a fuel system inspection performed by a qualified professional

When You Turn the Key to the On position, You should hear a momentary run of the fuel pump to prime the EFI to start the engine. Once the engine is running....Oil pressure should latch the Fuel Pump Relay to continue engine run....Check the Oil Level....A low Oil Level Sensor can disable the Fuel pump or ignition signal, Try to determine if a problem is fuel related or electrical........

If you can't hear your fuel pump priming then either, the pump needs replacing or the relay. If you replace the relay and you still don't hear the pump prime then it's the fuel pump.

Have you ever run out of fuel in the last few months, or run very low on fuel. If so replace the fuel filter.

Have you ever run out of fuel in the last few months, or run very low on fuel. If so replace the fuel filter.

you must be getting fuel, remove fuel line @ engine, have someone crank the engine, then you'll know, NO SMOKING ! if no fuel, check fuel pump relay ! check all fuses . pump should hum for only 2 seconds, when key is turned to ON position. to prime the system. always check all ground wires to fuel system. important ! good luck

have someone check your ignition coil.

Your fuel injector rails should have a pressure release valve somewhere. Pressure needs to be released. Watch out for flying fuel though!!!

have you chaged the glow plugs.They have to be working to start the engine from the key.