Can anyone help me with a troublesome home theater problem?

Gotta agree with cosmicbandito about the heat - it makes electronics do all sorts of funny things. Adequate ventilation is a must. On the sub, I'm trying to visualize (auralize?) the crackling sounds it's making. It sounds, to me at least, like a connection problem - I have this issue with bad cables between my syntheziser and amps. I'd change the cable first, not just the connector. It's cheap to do that, and easy. If the problem still persists, then you need to localize the problem: Can you hook up the sub to another system (a friend's, perhaps?) and test it out to see if it still does it on another amp? If it still does, and the problem follows the sub, you know you have a problem there. If it doesn't, then you might have a problem either with an amp setting, the sub circuit, or a bad cable, too.

I'll try running it in a more open area. It has a few inches of room on the top, but not much room at all on the sides, and the back and front are open. I could put a few holes in the sides of the cabinet, maybe?

It might be aesthetically odd, but see if you can rig a fan blowing on it for a while. Also - troubleshoot one thing at a time. Don't change more than one variable. You're in good shape if you can reproduce the conditions and problem every time.

I'll try the fan. It won't be ugly if it's behind the cabinet, right? I've had the receiver hooked up to nothing and on another circuit and sitting on a hardwood floor with nothing around it, and it powered itself off. This was before I brought it in for reapir, but still.

Hook the sub output of your receiver up to a regular hi-fi speaker* to test whether it's the receiver or the sub that's making the noise). (* I'm assuming from your comments that the sub amplifier is in the receiver)

Check that you have a constant, stable voltage coming out of your wall socket. I had a receiver and television that would sometimes turn themselves off. Turns out there were more than 120 volts coming out of my 110 socket, and I'm sure it was spiking from time to time as well. (The house I lived in was very old). I solved the problem by installing a power conditioner in my rack which insures constant, clean electricity. The particular model I have is the http://www.musiciansfriend.com/srs7/g=home/search/detail/base_pid/181304/. I got mine much cheaper than what's listed on the website at Guitar Center. Once installed, the LED's were constantly pegged in the red, but I got a solid 110 volts out of it, and no more problems with equipment shutting down. I know it's not a cheap solution, so you may want to try the ventilation options first, but to me it sounds like a power problem. Also, make sure your system is properly grounded. If you've lifted the ground on any of your equipment, start using that third prong.

Is it possible that there's a short in one of the speakers/speaker wires?

Well, I got the Monster Power thing which says it conditions the power. I'm not sure if it's as good as the one you have, but it says it evens out the voltage. Anyway, it still happened this morning. However, I don't think the circuit is properly grounded and I don't know what I can do to ensure that it is. I bought an outlet tester (plug it into the outlet and it has three lights that tell you what's going on) and it reported as hot/neutral reverse. I'm sure that's bad, but how bad? Anyway, the monster power thing tells me the line is protected (not grounded) and everything else seems to work fine. I don't know that i want to rewire the outlet, but I will if it will fix the problem. I'd rather my landlord take care of it, but trying to coordinate our schedules so he could come in and take a look has been troublesome. Could I buy a better outlet at Home Depot or something?

I suppose it's possible that there's a short, but I don't know. I ran it without any speakers attached and it still happened. I guess the short could be in the sub and maybe that's where the noise is coming from?