What's wrong with my car? (CEL, funny noise)

So, my check engine light has been on for several weeks, but I haven’t found the time to take it in. As of two days ago, the car started to make a funny engine noise.

You wouldn’t notice it if you didn’t know the car like I do. It’s sort of a hummy growl, and it’s “under” the revving engine noise - it’s independent of the gas pedal and I hear it pretty much the whole time the car’s running.

It’s a 2004 Pontiac Grand Prix. It would be nice just to get some ideas of what it could be, how much it could cost to fix, and if it’s a super crazy emergency (didn’t want to take it in around the holiday weekend.)

Is that enough information?

Oh, I was incorrect - on the way home I noticed it only happens when the car is moving. When I brake, it “winds down” and stops. If anything it sounds like a WWII bomber, oddly enough.