Assuming yours a ground potential related issue, you should try to isolate the culprit first. Try the following steps.
0. As Pogre suggested, lower the HCA 1205's gain and report back the effect.
1. Separate the AVR from the HCA 1205A power amp completely, electrically and physically.
2. Plug in the power amp to a dedicated wall outlet that has nothing else connected to it.
3. Hook up the 2 front main speakers to the HCA 1205S's output binding posts.
4. Turn on the power amp and hear if you still get the buzz/hum.
If the buzz/hum is gone or substantially reduced, continue to the next step.
5. Reconnect the preouts of the AVR to the power amp but leave all inputs disconnected.
6. Again, listen for buzz and/or hums.
If all is still good, then reconnect the inputs, but only one at a time, and each time listen for buzz/hum. The one that triggers the buzz/hum is the culprit.