RF Induced Humming??

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!

Ok Dave this seems a bit more complex that first thought. Not sure now how the cable's ground hum is getting into your rig, as it sounds like they're isolated from each other, but apparently they are not (unless of course as in when you connect the VCR to the preamp, that's an obvious path).
Cable systems are widely notorious for these problems, as their ground's potential isn't normally the same as the ground in your house. One other thing that I recall doing was connecting a small 20awg. stranded insulated wire from a wall outlet's ground screw to the Cable coax's ground sleeve. I wrapped about 2"to3" of stripped bare wire around the F connector's sleeve & fastened it with a wide nylon cable tie. This achieves a common potential of house ground to cable ground, & may or may not help you but it's an easy experiment & almost free if it works. If any of your AC plugs are reversible you could try playing around with that as well. I'm still not sure if I have your whole picture in mind so if I've missed something then do elaborate as I (or someone else) may think of other alternatives. Usually the hum-bucker is suggested, but looks like that caused you some other problems.
Thanks BTW for your vote of confidence; I try to help others here as they've helped me too. I'm willing to discuss this via phone too, if you're otherwise unable to find a fix just email be via the hyperlink so I can get the "whole picture". Good luck!

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.

Your info is a bit incomplete Dave but I take it you're plugging an audio feed from the TV into your preamp? I had hum problems doing that, but found an easy way out. Car audio shops have little audio isolation transformers with RCA's in & out. You can put the coupling transformer in line with your interconnects to isolate the ground. It's only TV sound, so who cares about the little bit of quality degradation? Still sounds pretty good anyway.