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I purchased a 1981 528i with an M30 out of a '79 and we've been working on getting it running. It's been sitting for at least a few years, but we've replaced all the intake gaskets and all the air/coolant/fuel hoses, as well as the ECU, wiring harness, and AFM. After cranking for a while, it ran successfully for 10 minutes (idled well, didn't need any throttle application) before we turned it off. It then promptly refused to start, and is producing no spark.

We thought it might be the ignition coil, and tested it for resistance across the positive and negative terminals. It showed 0 ohms of resistance (which I thought indicates a short, but if it's externally resisted then maybe not necessarily?), but we replaced it with the same part out of a friend's MB and saw the same result (both use the same Bosch part). We're thinking at this point it might be the ballast resistor for the ignition coil, but were wondering if anyone on here might have some suggestions.

I don't know if it's right, but my red-top coil reads 0.6 ohms and car runs fine. I can tell you those coils run at 8v or so normally, and 12v for starting. That's all the ballast resistor does, keeps it at ~8v or so, bypassed to 12v during cranking for a better spark.
So for troubleshooting you could short/bypass the ballast resistor and run it at 12v and it will run (just don't leave it like that or the coil will overheat and burn out). If it took a while to start maybe it's not bypassing the ballast resistor during cranking.
Either way, if there's now no spark, maybe somethings up with your wiring or ignition module?

Oh, sorry, forgot to mention we replaced the distributor cap and rotor.

Thanks for the tip on the resistor! We'll try bypassing that and see if it works. We were wondering if maybe it wasn't providing the right voltage when it was cranking.

Update: the car successfully turned on and ran for a while again after sitting for a week, but it now is refusing to start as before. The car was refusing to start after sitting overnight last weekend, so it does not seem to necessarily be a hot start issue. It has successfully run with two different ignition coils, two different AFMs, and two different combo relays.