Although your problem doesn't ring a bell with me, there are a few things to consider. Have you tried to start the engine in "limp home" mode? With the ignition off, disconnect the AMM, then try starting. If that does it then the AMM is likely going/gone (but clean up the connector first just to make sure). You likely have the LH 2.2 system and in that case there is a 20 amp fuse for the fuel injection system (on the 240's it was under the hood and was very troublesome). You'll likely find that fuse in your console fuse panel. Pull the fuse and make sure the fuse isn't oxidized and that the fuse socket isn't showing signs of overheating. At the same time, if your fuel pump has been working hard (like the in-tank pump is gone or the main pump is on its way out) then its fuse socket can also get overheated (this is more common on the 740's). You really need to pull the fuse panel right out and inspect from below to spot this one. The next most likely thing I can think of is a troublesome Hall Effect sensor in the distributor -it can give all kinds of grief when it's starting to go. I rather suspect you'll find the latter is the problem.
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Dave -not to be confused with a real expert