If it had an inertia switch fitted and it had tripped then it wouldn't start at all until the switch was reset. If it starts but won't stay running then it sounds more like a fuel supply problem. Check that the fuel pump stays running with the ignition switched on.
My thinking is that after the initial start-up, the ECU takes over and the fuel pump is cut off when the ECU thinks the engine isn't running (to stop fuel spraying everywhere after a bad crash).
Guess the fuel pump is active when you first turn the key for a few seconds?
I agree with Louie - I believe that the function Louie's describing is performed by the Bosch fuel injection system power supply relay. At least, it is on the Mk1.
The special relay (has a circuit board inside) is a tall type mounted near the battery on the Mk1. I'm not sure about the Mk2 but knowing that it's also Bosch, it may have a similar component.
The overboost switch may be corrupt. It is located on the left side of your inlet manifold and had 2 wires attached to it. When this switch makes contact it stops your injectors from spraying petrol. Normally it makes contact at >1 bar boost to prevent the engine from overboosting.