Greg,
Yes, and your DME is on the wrong side of the car too...
I think trying your DME in another car is not very likely to harm any of the rest of that car, and will tell you very quickly of your DME is good or bad.
I agree with Ingo, if you found and replaced a bad resistor, well that was a symptom, not a cause of your troubles. Resistors burn because too much current is forced thru for some reason...
Hope you get to the root cause soon.