Well, I reinstalled a saved system image that was about a month old. I'm positive it was clean, and I was not experiencing this problem at the time that image was created. As soon as I reinstalled the image, I noticed that the problem was still there. Now I'm really stumped.
I was thinking about the issue and thought that perhaps it was related to my keyboard since there are characters mysteriously pasting about every 30-60 seconds. I uninstalled my keyboard
driver (Logitech), and unplugged it from my computer. Before doing that I opened an empty notepad file. Even with the keyboard uninstalled and unplugged the pasting of random characters continued.
I'm very frustrated at this point, and I'm hoping someone can help me. I've never seen anything like this.