Fuel pump wont shut off

Why would it have a switch? Fuel cut off switches are found on race cars. The closest thing you probably have is a fuel pump relay. As for the location of that, this thread is good: http://forums.nicoclub.com/1984-300zx-fuel-pump-relay-location-t567634.html

Check the fuel filters and change them IF the fuel pump ran dry it might have worn itself out. You need to have the fuel pressure checked.

Sort of.
There should be a relay that provides power to the pump when you first turn the key on.
Then once the engine starts power is provided by way of the oil pressure switch. That way the pump won't run in an accident.
The oil pressure switch grounds the fuel pump relay on some models.

a oil gauge reading maybe delayed until car starts and builds good oil press.Did you check for spark
was car running good before this happened? Do you have a rpm reading when cranking car?

About the only thing left is the Ignition Control Module.

if it started after using starting fluid, then it isnt the fuel pump. prob a water temp sensor

Are you sure the new belt didn't jump time? How was the belt tensioner when you replaced yhe belt? Did your water pump leak onto or into your crank sensor?Are you sure you have proper fuel pressure?When you replaced the timing belt, did you make sure to find top dead center on cylinder 1 ? Just lining up the timing marks may not have worked if this is indeed what you did.If you had the crankshaft rotated 180 degrees, your motor would be trying to fire on the exhaust stroke, instead of the compression stroke. To find T.D.C. disconnect your battery,rotate your crankshaft until the piston that is marked #1 in your firing order is at the top of its stroke, this can be accomplished by carefully inserting a wooden or plastic dowel into the sparkplug hole of cylinder#1. The dowel will rise with the piston and at the point where it starts to fall will be T.D.C. Now your timing marks should line up,and you will then be on the compression stroke. good luck! hope this helps

pull the transmission. remove the torque converter (automatics) or clutch and pressure plate (standards), the bolts for the flywheel are under that. make sure you replace the flywheel with the proper one especially if it's a standard.

This is more complex and you won't find anyone to give you advice. Dealer solution on this one.
Sometime they don't even know and guessing.

Maybe it's time to buy another car?

may wanna check the distributor could be outta whack (timing).