I've had the same problem before. It was the Air MAss Meter. Un-plug it and see if it will idle. If it does, replace the meter.

Do you mean that it fires while the engine is cranking, but dies when you let off the key, regardless of what you do with the gas pedal?

If so, then Strayhorn is leading you on exactly the right track. I've never looked at the ignition power circuit, and I don't recall seeing a ballast resistor on these cars, but one way or another, I think that it should be designed to get full battery voltage to the coil in cranking mode, but reduced voltage to the coil in running mode. That means that there are two separate circuit to feed DC voltage to the coil, and your "running mode" circuit is not working.

1) Check Strayhorn's wiring harness plug suggestion.

2) If you have a ballast resistor, check it for continuity. If you don't have an ohm meter, you can check the resistor by bypassing it (temporarily) and see if the car runs.

Here is something that happened to me and was really a head-scratcher until my mechanic (the great Neil Becker of Durham NC) figured it out:

The power to the ignition system on my '82 240 runs on two different circuits - one for starting and one for running. Turns out there was a short in the running circuit. We traced that to a bad plastic connector in the line, which was hard to spot because the connector was under the housing for the front right shock absorber (it's the top of the shock/spring unit, in the engine compartment - you'll see that several wire cables run through this housing for some reason).

We replaced the connector and all has been well since.

Hope this provides a little help.

If you need an AMM, I have one I got from a junkyard. I tested it on my car and it works, but my problem ended up being the idle motor. So, I have an extra AMM. You can email me and we can work something out.

I would think AMM. With ignition off, start it and see if it runs (idles) fine. If so replace the 007 AMM with a good used one for $75 or so.

Check out the Idle Air Control Valve.
If it's cold out and this thing is dirty the car will start up and then die unless you hold your foot on the gas until it warms up a bit.
I'm about to do this on my 89 240. I had a similar problem with a 88 740 and this cleared things up.
Look in the FAQ's for 740's. It's in there somewhere.

Good Luck