Car hums but won't start?

My car was starting fine this
morning, then in the afternoon I went
to start it and it just made a humming
noise but didn't even turn over. The
humming sounded like it was coming
from the back of the car. It would
hum not just when I was turning the
key to start it, but as long as it was in
the "ON" position.

I'm not sure if this is related, but
about a week ago, I had the IAC
valve replaced because the car
would stall immediately after starting,
and it seemed to fix the problem.

I ended up paying $50 to tow my car
back to the mechanic that replaced
the IAC valve, and they called back
saying that they started it about 15
times with no problem.

I've done some searching, and a lot
of people suggest that it could be
the battery contacts or the
connection to the ground. Other
people say it could be a bad starter
or solenoid, whatever that is.

So I'm leaving the car with the
mechanic over the weekend, hoping
they can actually see the problem.

What could the hum be? Advice?