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Well if the lights were working then first I'd make sure it was an identicle module and that it was plugged in correctly.
Do check that the proper bulbs are installed......
With the bulbs plugged in they will show some continuity to ground with resistance, set your meter to ohms.....with the bulb out there should be no reading at all, this is providing the cirquit from the bulb to the module is a strait shot.
Does anyone have a schematic?
My friend tim has 2 e30 m3s.....I'll see if he can look at his manuals if we can't dig it up.