Can you hear the fuel pump starting when you get someone to crank the engine? If not, check fuse & relay and also suspect crank sensor, I'd say. ECU will only energise the fuel pump when it detects cranking.
If pump is running, have you got fuel pressure? Loosen the flow union from the fuel pump to rail and see if fuel escapes under pressure.
Have you tried cranking it with foot on floor for a few seconds? Just thinking if an injector has leaked and flooded it?
If there's no fuel pressure, it could be that it has sucked air due to the low fuel level but needs considerably more in the tank to prime the pump.
Try taking off the flow line to the rail and extending it with some fuel hose into a can, then crank the engine so the pump can prime with no restriction to flow (i.e. it's not pumping against the FPR so may prime easier). Make sure you get a solid stream of fuel here, then reconnect.
Then disconnect the return line from the rail, extend the union on the rail with a length of fuel hose into a can and check you have plenty of flow here.
Indicentally, if you want to run the fuel pump without cranking the engine, take a short length of cable with a spade connector on each end and short the two wider pins on the fuel pump relay base. Be very wary of generating a spark with fuel vapour around, of course.
I assume the LPG wiring doesn't break into the fuel pump circuit? Mine certainly doesn't. Fuel pump runs as usual on LPG.
I'd be surprised if it were the injector signals because unless there's a major problem with the LPG ECU you would only lose one injector as they're individually switched. Would be worth checking the supply to the LPG ECU, although even still, I'd expect it to loop through the injector signals if its' supply failed. Mine certainly does.
Kevin