I'll see if this info can become a sticky for E38. Are you sitting comfortably with a coffee - good. The E38 has a multi layer wafer ign switch. One of the layers sends a VOLTAGE to radio/nav etc systems to get them into stand-by mode. The CURRENT is so low the contacts oxidise over time. It has been known that turning on the sun visor vanity lights can fix the problem as they use the same contacts. To fix: Remove the electrical part of the switch and take it out of the car. Drown it in switch cleaner and operate it over its full range a number of times. Wash it out (with the cleaner) an blow dry with compressed air. Refit and all should be well. If not it's another problem on the same circuit. Then you will have to trace with voltmeter etc..
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