Well you were in the right faze of mind there. These 2 sensors will let engine start, not let it start or shut engine down. But for the 2 sensors to work how they should, they should have the correct voltage going into them so they can output the required voltage to the ECU for engine to be allowed to start. The crank one may not be powered though. So what I am coming to, is, Battery output. Is your battery good, quite new, how old. As its not just these cars that need a good battery to satisfy the starting parameters... Somehow it doesn't sound fuel pressure related, but just might be.