[tommyweaves]

My money would be on the main fuel pump in the fuel tank.

Sometimes referred to as a "lift pump", its job is to supply fuel to the high pressure fuel system. Sometimes the bearings stick. They sometimes get a bit noisy before failing completely.

If it starts running when you start up, it'll keep going, but if it decides to jam at start up then it'll do nothng. Sometimes a thump on the tank is enough to free it. If it sticks whilst you're driving there's often enough "suck" from the high pressure system to keep supplying fuel. Which is why it only shows itself as an issue at start up; and intermittently.