My 1987 300zx cranks but wont start.

You need to reset the fuel pump inertia swich in the trunk.

check the fuel filter? that could be clogged

Be sure your fuel filter isnt clogged also check the fueses if both of these are ok check the crank sensor it sends information to the pcm telling it you are trying to start the engine it then sends a signal to the injectors to spray fuel but if the crank sensor is bad then the pcm doesnt know you are trying to start the engine and therefore never sends the signal to the injectors to spray fuel.

Have you changed the fuel filter.

Your pump may be priming but the pressure could be against a clogged filter.

You might want to check the fuel pressur at the rail.
It might be a fuel pressure regulator problem

could be the pump? or the pump relay? or even a clogged fuel filter crack the line going into the rear of the filter and crank the motor if fuel comes out ? change the filter if no fuel then? check the relay and or change the pump

the filter on fuel pump might be clogged as well or fuel pump needs replaced

The number one problem with these cars is with clogged fuel filters. They must be changed regularly. When you say it won't start, do you mean it cranks but won't fire? That could be a fuel pressure problem due to a clogged filter.

check the fuel filter. If it is clogged it will do just as you are saying. has enough presure to run car however when you press gas the filter isnt letting full pressure go through filter because it is clogged. If any questions email me. Good luck. Change filter.

check manual for a fuel system reset switch .good luck

Crank position sensor bad?
Are you sure the fuel pump is working? Might be the sending unit in the fuel pump that is bad. Clogged lines, clogged fuel injectors, clogged fuel filter, all things that could be checked.