I had that happen on my Audi; the return spring in the ignition switch had broken, and the key was not returning by itself. As a result, the starter motor was not switched off.
The humming I heard was the starter motor going for a ride!
My short-term solution was to help the key back to the "ON" position from the "START" position.
The long-term solution was replace the ignition switch.
Engine and starter are still doing fine!
Good luck, and good hunting!
'96 E300D 60k mi (wife's daily ride)
'95 Audi 90 120k mi
'92 GMC Suburban 139k mi
'85 300SD 234k mi (my daily ride)