You are on the right track. Have you tried the radio(s) out of the car on test speakers? That way you will know if it is the unit or the car.
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL (X 2 - 1 White and 1 Light Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i