Power conditioner needed????

For not all that much you can get a Monster or APC unit designed for home theater with dedicated outlets offering component specific filtration. It makes a big difference and for a few hundred bux its less expensive then many alternatives.

FWIW I have always found that video displays benefit the most from power conditioning.

You could also try upgrading the cables from the sources to the display or the receiver and then to the dispaly - I doubt that it will fix the problem but it might make a nice small difference once you do...

What happens with the raster when there's NO input connected at all? (this could be a way to trace the interfering source).

If you have any GFI (Ground Fault Interrupt) distribution panel breakers or GFI outlets in the house, they too might be a problematic source of your RFI (radio frequency interference). Flourescent or halogen plasma lighting can even be an issue, but apparently not in your case

At one point, the only breaker that was still on was the one for the TV.

Regarding possible differences of ground potential on your incoming RF coax: you can try grounding the shield connector by stripping a few inches of small conductor (#22 awg or so) insulated wire & wrapping that around the F-connector shield, fastening it with a cable tie or tape wrapped around. Then connect the other bared end to an AC outlet cover mounting screw, which typically ties electrically to the AC outlet's ground. Or you can go right inside the outlet box & pick up the AC ground connection directly.
I've had to use this shield grounding technique for video hum bar problems; others have used it successfully too. Your situation seems a little different, but this is simple & easy to try.
You can also try completely isolating the coax by connecting two antenna matching baluns directly back to back (available at Radio Shack). The incoming coax connects into balun #1, then the 300 ohm twinleads tie directly to each of balun #2 twinleads. The 75 ohm isolated coaxial output is then taken out of balun #2. This is inexpensive & introduces some small signal losses, but if you have signal to spare then it's not a problem. There's a $100 coaxial isolation box available (from MIT?) that may or may not(?) introduce smaller RF losses. Sorry I don't remember those specs or the brand for sure.

There could even be a source of external RFI getting into your equipment (nearby radio station transmitting tower or cell phone tower). Or a neighbor's CB radio or Amateur Radio transmissions. That might need to be shielded or trapped out. You can try a product from Audioquest called RF Stoppers. Basically they are split ferrite rings that come apart & snap together around your cabling (RF &/or power cables, etc). There are two levels: the Juniors & the Regulars, which are twice as thick & yield more RF filtering attenuation. Various diameters (I think?) are available. I saw a similar product at Radio Shack years ago; might still have them too.

AC line conditioning is also worth trying of course. If the power cord is a detachable IEC type, some upgrade AC cords even have built-in filtering (such as JPS, MIT, or Custom Power Cord Co.) and many others. These cords have sometimes been reported to significantly improve video quality, even where interference is not an issue. Search the forum archives for specific posts in that regard.

Baffled

I don't know about the radio transmitter thingy... it would have to be real close given the FCC regs on output transmission power but not everyone plays by the rules in that arena.... it'll be easy to find out... simply look for the tower/antenna. it should be pretty big/tall.

Back in the 40s, my folks were in Biloxi Mx. at Keesler AFB. They had an apt. off base. My mom would play the radio on her fav station. Now and then she heard some other conversation coming over the radio ch a bit garbled and in a different language.

She told someone on base about it as she worked for the PX, and my Dad was in hte USAF. it turned out someone else in that same apt bldg was transmitting info about the base to another location... so she inadvertently helped capture a spy by paying attention to her radio.

While you're looking over your grounding, check carefully for loose &/or corroded connections. Disassemble the clamp where the ground wire connects to the rod. Burnish the top of the grounding rod with a wire brush, emery cloth, fine sandpaper etc, exposing clean bright copper. Burnish the bare end of the ground wire too. Before reassembly, liberally apply some silicone paste such as SilGlyde (NAPA auto parts supply shop) or NoAlox paste (electrical supply shop or larger hardware store) or even automotive or marine bearing grease will work; this prevents the connection from re-oxidizing. Also check & clean the opposing end of the ground wire; whatever it connects to. Look for loose fasteners, apply paste, snug down the setscrew, etc. Check your house power ground also, if you can access that. Check the neutrals & ground conductors in your house power distribution box and all conductors at the load outlet for tightness & oxidation.
You say ground rod(S), as in more than one? Multiple grounds could be a cause of ground loop noise, as per Jim above. This can also be a lightning electrical hazard due to differences in ground potential. You could try running all connections to a common ground post, or tie them together electrically with reasonable size conductors (#14 awg solid).

isolating the coax by connecting two antenna matching baluns directly back to back (available at Radio Shack)

A balun is a simple RF transformer. 300 ohm balanced twinlead connections at the (typically input) side (usually connected to a TV or FM antenna)
and 75 ohm unbalanced coax connection at the other end (typically output) side; they will work in either direction though. You would need two as my previous post. Ask at Radio Shack. Also available at Lowes, Menards, Ace Hardware.

If you don't understand RFI etc & want to learn more, then link to my Audiogon member email & leave me a phone contact. I am a federally licensed RF technician.