[Allldi]

If you can start it every time by compression starting it, then I doubt that the alarm is the problem. The reason why that shop didn't charge you labor for the DME relay is because it takes about two seconds to change. That shop may have knocked something lose on your starter when they were doing your motor mounts. If you can get it back to them, they might be willing to at least look under the car at the starter for you for free since it's possible that it's their fault. If the battery is fine, and the car runs fine when compression started, and all of the fuses are fine, and the starter doesn't even operate when the key is turned, then I would think that somehow the starter motor isn't getting electric current. I would think it's the starter motor, the starter solenoid, the starter switch, disconnected wires, or something along those lines.

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Ryan
1991 944S2 coupe