I'm with you. I've been right where you are. First off, hook the system up in an alternate way so that it works when your wife wants to use it. That will eliminate excessive noise from that component.
For now, connect Tivo with component cables and digital audio if you can, then you'll have time to think, test and work out the HDMI issues without your wife knowing anything is wrong.
Once the Tivo is at least working, the only immediate issue is the humming. Go through the ground loop procedure and make sure it's not that. If the sub is not plugged into the same circuit as the rest of the system, try running it from the same circuit. If that doesn't help, diagnose it one step at a time. Disconnect each component and see if the hum goes away. Try a different cable on the sub too, just to check and see. If you have no hum when the sub or Tivo is disconnected, that's the source of the hum.
I won't pretend to be an expert on this stuff, but this site seems pretty slow on weekends and I know how frustrating it is to have a problem and nobody to turn to, so I'm just saying what I would do in this situation so you don't feel abandoned.