Power supply noise.
Assuming the equipment itself is not defective, which is a pretty safe assumption as the buzz has come and gone before, the source of the noise is most likely within your household circuits.
Remember what I said about chasing an "electrical ghost".
When I was a kid, my moms vacuum cleaner and sewing machine would make a huge amount of static on my TV.
Same problem goint on here.
As you said, the only change you made was switching the HVAC from AC to Heat.
Making an assumption about your HVAC.... you have heat strips or another source of radiant heat within the HVAC. Those heat strips pull a relatively large amount of power and are prone to generating electrical noise that is transmitted to sensitive electronics that share the same household circuits.
The easy way to solve the problem is with a decent quality power strip with built in noise suppression & surge protection. Monster Cable, please their expensive hearts, is a decent product and available at Circuit City, Best Buy, Tweeter etc. Similar products are available from Belken (sp?) and other companies and are available through Office Depot, Sears, Lowes etc.
By the way, Belken is pretty good stuff. I have it on all of my computers.
There are more expensive ways to solve the problem, including, gasp, replacing the heat strips with newer, less noisy designs, as well as installing noise suppression on the power/ground wires of the heat strips.
Add a $30 to $50 power strip and lets see if it solves your problem.
If you already have a power strip (surge protector) and it is inadaquate for your noise isolation needs, it is most likely because it doesnt have any noise suppression in the model. Many of the lowest priced units have zero noise protection.
Don't buy the most expensive model on the market, as most of the entry level units will quickly solve this type of problem.