The pressure transducer that controls the flow of the fuel injectors is notorious for diaphragm failure. Its a hand grenade shaped item with about a 1/4 inch vacuum line. To check it remove the hose from the manifold end and suck on it. If it doesn't hold a vaccuum, its got a perforation. This gives you a full rich mixture and leaves you in the "limp home" mode of operation.
Depending on other conditions it may not relight after failure. If the car backfired at all before it stopped, this may be a likely cause.
The other and perhaps more likely source of problems is the contact set in the base of the distributor. You can remove the electrical connector at the distributor and put an ohmmeter accros the connection (I think there are three)
and then crank it; you should get alternating open and closed circuit.
The other problem I had with mine was when the bakelite fiber camshaft gear failed, which lives you with no cam action. Open the breather and observe the valve action as you crank the engine. If nothings is moving, that the cause.
These are three reasons I can think of right away.
Good luck.
Dean, Folsom CA