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what do the traces on the bottom of the board look like? if the resistor popped it could've burned some traces too......
bad grounds can cause all sorts of problems, it's the one thing german electronics don't like.....

did the other module have the same failed resistor?

follow the traces on that resistor and see which plug pin it goes to, then see if you can identify which wire in the car it goes to, this will give some direction....resistors don't pop for no reason, and you said it....too much voltage...

just a thought.....since you have your meter out check the voltage at the battery when the engine is running......just to make sure it's not overcharging....