All the LPG systems do is slave off the petrol ECU - they don't take over running of the engine. When running on gas, the LPG ECU shuts off the petrol injector feeds and emulates them to the petrol ECU (so it thinks it's still injecting petrol). The LPG system (if the more common sequential systems) then applies a fiddle factor to the measures petrol injection time, to account for the fact you need a bit more LPG for x quantity of petrol. The LPG ECU then fires the gas into the intake, where it's sucked into the cylinder, boom, and well, that's basically it.
So the fact that it runs on LPG shows that fundamentally the engine ECU is working to run/control the engine.
Which means that your issue is in one of 3 places (in my mind) 1) the LPG ECU, and what's happening is it's not reconnecting the petrol injectors to the petrol ECU when it's not running on gas. This to me is unlikely, as they generally use relays to changeover the signal from 'connected' to 'emulated' with the 'Normally Closed' position (IE relay not powered up) of being set to the petrol injectors being connected. So even if the LPG ECU loses power, then the petrol injectors will still have a connection and allow running on petrol. It's not impossible the LPG system is messing things up, but I'd say it's highly unlikely - especially on all 8 injectors.
#2) is that you have a fuel delivery problem. Either the pump/relay/ECU isn't doing something properly... If the pump is nearly new, and there is fuel at the rail (what fuel pressure do you get when it's running? Even if it's running on LPG, the fuel rail should be pressurised - so it's worth checking that with a gauge, and also seeing what it does when you hit the button to change back to petrol)
#3) your petrol ECU has a weird fault in it.
I somewhat doubt that the petrol ECU is the issue - if you say it's holding the fuel pump relay in when it's running on LPG (which it should do as it thinks it's still running on petrol) then any other problem with the ECU would show on LPG - if it was ignition, crank sensor etc related, as it's all still used when the vehicle is running on gas.
Fuel delivery (somewhere) is my bet. If the pump is running as it should then it's either not producing enough pressure, there's a blocked fuel filter, or maybe even the pressure regulator on the fuel rail isn't working properly...
Put a pressure gauge on the fuel rail and see what pressure you get when you start it up on LPG, and then see what happens when you switch to petrol.
If fuel pressure is in spec, then it points more to the injector side of things. but then again, 8 dead injectors isn't likely, or even enough dead injectors to stop it running badly would be likely - more extremely bad luck..
