Havn't had to repair mine yet. Is there a switch the lever hits in 'M' mode? Is it damaged? Is it connected? Could a PO crossed up some wires? You may need to download a wiring diagram. A careful look round may solve your problem. If you join those wires does the 'M' light come on?
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL (X 2 - 1 Alpine White and 1 Glacier Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i