Sounds like the hall sensor in the distributor has crapped out. The insulation goes bad and they fail to produce a signal to the ignition system and therefore also the fuel computer. No trigger, no fuel pumps and no firing the injectors.

Replacement of the distributor is the easiest option. It's also the most expensive. You can get a dist from any 84-88 740 or a 740T/760T up to 89. You need the one for LH 2.2 fuel injection. There's a simpler one for the later cars that is less expensive, because it does not include the hall sensor.

There are replacement sensors available- I've never installed one but it's more involved than simply unbolting and plugging in a replacement distributor.

Look for a 740 in a junkyard or call FCP Groton. You probably don't want to know what a dealer gets for one of those.

You can confirm this is the failure by either wiggling the connector on the bottom (not the coil wire, the plug) and see if the car will start; or simply pull the coil wire and see if there is spark during the times the car won't start. If there IS spark, then I'd move on to the fuel pump relay (always a suspect) and if that doesn't do it, call the shop.
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Rob Bareiss, New London CT ::: Roterande Fläkt Och Drivremmar!