Ok you may want to start from basic principles and double check the following:
(Please ignore if you have already completed the following and still not start)
FFR Installation instructions are the latest version
Inertia switch is engaged
Fuses in chassis fuse box are good
Gas pedal, ECU, 02 sensors and MAF are properly connected (any one of these could/will cause a failure)
Wiring connected as per FFR instructions
Clutch safety switch is bypassed (if not using) blue wires are connected together – see photo
DSC02181_1.jpg
Chassis harness orange wire and blue wires are properly connected to Coyote 12V Start/run wire (red/green) and 12V start wire (red (blue) respectively - refer to photo
DSC01635_1.jpg
PCM is wired as per FFR instructions
Neutral safety switch from Coyote harness is routed to ground
You mentioned the fuel pump turns on so – no issue there
All grounds properly connected as per instructions
If after double checking these the problem is not resolved, you will need to test starter relay and other components for failure.
Hopefully it is the inertia switch