Well, after many hours of relocating equipment, trying other equipment, checking grounds, and unplugging various items around the house trying to find the culprit, I finally found the problem.
I had an X-10 remote transceiver in my attic and another in my basement that I haven't used in a long time and pretty much forgot they existed. Unplugged the one in the basement and the problem got much better. Crawled up in the attic and removed the other and the problem went away all together. It's been running trouble free for several days now.
Duhh...Now, looking back, I don't know why I didn't think about that first. The way the X-10 stuff works is by sending a signal (noise) through the household wiring. I thought it only sent a signal once it received a command from the remote but apparently it puts out some noise most, if not all of the time.
Thanks to everyone for all of the suggestions!