RF Induced Humming??

You're correct, I have an RCA connection from the VCR to the pre-amp. If I unplug the RCA connectors that run from the VCR to the pre-amp, the humming stays the same (with the cable still plugged into the wall with no ground breaker). I would not mind sacrificing TV sound to eliminate the hum, unless that means getting rid of the TV and cable altogether! Thanks again.

Brilliant! You nailed it! The cable was using the shield as the ground and that was causing the humming. I don't fully understand the physics, but the solution is simple. I found a coax grounding block ($2 at ACE hardware), which basically replaces the task of having to strip the coax and wrap a wire around the shielding. The block allows you to connect the coax going to the cable box in one end and the other end to the jack in the wall. It has a small screw on the housing that you attach a wire to and then attach that wire to ground. I have an AC outlet near the cable jack so I attached a small length of wire from the ground screw on the coax grounding block to the ground of the AC receptacle (my AC receptacle is grounded by the mounting screws going into the metal receptacle housing which is grounded, so I just attached the wire to the receptacle mounting screw leaving the AC outlet unobstructed). I turned everything back on and SILENCE!! It worked perfectly. No humming at all. And my local TV stations come in fine and the cable modem connected. Thank you very much Bob, wonderful advice!