THis is where I would start although I have not had this problem (yet....). Check all the plugs, terminals and earths for the units in the dash and boot (trunk for the other English speakers). The fact the radio makes a noise tends to point to not getting the RF part of the signal rather than an audio problem. A plug out or wire off may be your (simple) problem..
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i