Engine wont start, fuses and relays good, good fuel pressure and turns over nicely

When you turn the key to on, not start, do you hear the pump turn on for a couple of seconds to pressurize the fuel system? If you do, check fuel pressure with a gauge, should be over 50 psi if multi port injection, about 20 psi if throttle body injection. If pressure is good, you may need to check the fuel injector circuit.
If no sound from the pump, you will need a voltmeter or a test light to check the fuel pump circuit. First check the fuel pump fuse. Then check for power at the gas tank on the fuel pump wire, when the engine is being cranked over. Power should be going to the pump then. If nothing, move back to the fuel pump relay-need to check for power at the relay.

If you have no fuel pressure at the engine when key is on, the pump is not coming on. Check fuel pump fuse, check fuel pump relay (relay should click when key turned to on-put finger lightly on it and feel for click when someone turns key to on). If no click, signal from computer may be lost, ground for relay may be lost, or relay may be bad. If it clicks, wiring from relay to pump may have failed, or the relay's main power source may not be there at relay-find the fuse link or maxi-fuse that powers that relay. One terminal at relay should be hot at all times-can check for that with a test light.
If pump is working and you do have fuel pressure, you will need to check injector circuit. Post back if questions, or need further help.

most likely you have a bad crank sensor or fuel problem you need to check fuel pressure ,if you have enough pressure ,most likely you need crank position sensor,if you don`t have fuel pressure ,it might be your fuel pump relay or the pump, i would start with the relay first very unexpensive. you can also hear the pump if it`s working by cranking the engine and listening rear of the car for a humming sound .
good luck

Did you reset the inertia switch that shuts pump down in case of collision?

Voltage drop test the electrical circuit , do know how to do automotive electrical testing . Lose connection , resistance in the circuit , lose ground Mastering Voltage Drop Testing with Pete Meier and Jerry Truglia Testing Electric Fuel Pump Problems with Voltage Drop Test

I'd have to test when problem is ongoing. When you first turn on key, no crank, you should hear the pump run for a few seconds then stop. For initial prime, the computer doesn't need rpm signal. Engine cranking, the computer needs to see rpm signal or it won't ground the fuel pump relay. W/o rpm signal, no spark at the plugs and no fuel injector pulse. I know your talking about fuel, but, when problem is ongoing, check spark and fuel injector pulse, engine cranking.
Intermittent problems are a pain, have to test when problem is ongoing.

Not guessing as to what the problem is , testing for voltage drop problems with a volt meter . posted a video on youtube yesterday . If your still looking for guesses forget it , no one on here could say for sure without testing the circuit an hooking up a scan tool to see if PCM is energizing the relay . Do yourself a favor an take it to a qualified repair shop . Fuel Pump Electrical Circuits Description and Operation If you can't learn how to test from this guy , better take to a repair shop .

year and model and engine size if applicable

Do this test first. With the drivers door opened in a nice quite area turn the ignition key to the ON position without starting the engine. You should hear the fuel pump operating for 5 seconds which is priming fuel to the engine. If not heard the engines oil pressure sensor is at fault. The third wire from this sensor links to the fuel pump to prime. When the engine reaches normal operation oil pressure range the computer shuts off that circuit and turns on the fuel pump relay for the pump to run. That relay stays on until you shut the engine off

You have a problem in the fuel pump relay circuit for sure then. I'm betting the relay, but it could be that dropping resistor.