I'd be almost certain it's the crank sensor. Easy to replace and not expensive. When it fails, more often that not, it doesn't show a code.

 

 

not effectively without an oscilloscope. The crank sensor produces an on/off waveform to the ECU. no good way to test without seeing the waveform.

 

If the tach isn't showing 300 rpm or so when cranking that's a sign. If the fuel pump comes on for about two seconds at key on and then goes off but doesn't come back on when cranking that's a sign - you can check the socket to see if it's getting power.

When the ECM sees a crank signal it turns the system relay back on so anything like the coil, injectors etc that receives 12V from the relay and isn't getting it indicates the relay is bad or isn't being turned back on. However, if the pump primes at key on, it's not a bad relay.

 

Ed has a good point about a CPS check. The timer in the relay fires the fuel pump for two seconds at key on.
After a revolution of cranking, the CPS sends a signal to the ECM that turns on the ground to the fuel pump which cuts it on.

Problem is, you cain't really hear it while cranking.

 

 

You must have put the wrong relay in or the fuel pump is bad. Jump pump at the tank to see if it runs. My guess is you do not have power coming to fuse box or fuses are bad or their connection.. Has someone done some jumping with wires to enable it to crank like it is?