'05 E320CDI: Something's Running
 

I can hear it this morning in the garage, like a tiny motor running, barely. Seems to be in the rear or underneath the rear of the car. The check engine illuminated yesterday, although performance seems unaffected.

Randy, it's probably the vacuum pump under the rear seat. The pump is typically surrounded in dense foam to muffle the sound when it's running.

What is it's purpose? Should it be running after the Car has been idle all night? Note that my Car is pretty-much the base car: no navigation system, no super seats.

Randy, the MB vehicles I own rely on vacuum to operate the power door locks. If there is a major leak, or a loose connection in the vacuum system the vacuum pump will run continuously because the shut-off switch will not activate due to low vacuum.

I'm not so sure that new of a car still uses vacuum for door locks.

The fuel pump might be running, I'm not sure if that year of a car had it in the tank and not under the car like up to 2000 ish cars.

In any event, start probing around.

Problem Solved! The sound was coming from the area in the trunk, on the driver's side behind the fuse bod: some sort of hard drive or similar device. I pulled two fuses and left them out overnight, then put everything back, and no more problem plus the radio started working again.
I think Fuse 6 did it.

Are there any numbers on this box? I wonder if this is the cell phone system.

Fuse f6 40 amp that you pulled reset the audio gateway (the box above the wheelwell) which restored the radio,
When the radio locks up again repeat procedure, a few minutes will do the job.