Through the magic of the internet I determined the most likely failed component (the power supply board), then opened up the TV to look at it. I didn't detect any blown capacitors or obviously fried circuits, but when I found someone in Arkansas selling used replacement boards on Ebay for $18 I figured it was a solid gamble to just replace it and see what happened.
My trusty home repair assistants. They took care of the packing peanuts and bubble wrap while I handed the TV.
For once, a fix was almost as easy as possible. One bolt holding the back panel of the TV on was sticky and I wasn't able to remove it without significant cam-out of the Phillips head (they should have used Torx, Phillips was actually designed to encourage cam-out to discourage over-torquing before the advent of accurate torque wrenches - fun bolt fact of the day) so I tossed that one, but there are about 20 screws holding the back on so losing one is not a huge deal. There were only three connections to undo and redo and all of them had solid, clicky connectors instead of being obnoxious glued on ribbon cables or anything. Made the connections, didn't ground any capacitors through myself, fired up the TV and it worked, so I replaced the back panel and we were back in business. I seem to have lost my settings (probably the reserve battery was on the board I yanked so the volatile memory of the TV blanked) but they weren't a big deal to put back in.
For $20.50 with rush shipping and only a couple hours of my time total, counting research, I feel pretty good about that repair. Apparently unless the panel itself goes, repair of modern plasma and LCD TV's can be pretty approachable, especially considering I only saw estimates in the $200-300 for an initial diagnosis of a TV problem, plus at least $100 for someone else to make this fix for me. I could replace every board in that thing several times (at used part prices) before meeting the cost of having someone look at it. Good to know, especially since there is a 5-10% chance that the board I just put in has the same flaw as the original and will die in the next year or so. If it goes I'll just buy another one and slap it in.
Victory was tempered, however, by a further example of conservation of the to-do list. After replacing that food processor component but before fixing the TV, I had the furnace guys in for an annual service. Apparently since the spring when the AC guys looked at the AC coil the coil had developed a leak, which either overflowed or otherwise escaped from the AC drip pan and drain...and dripped down onto the furnace heat exchanger. It rusted and is beginning to crack. Carbon monoxide levels are a long way from dangerous but are above legal limits coming out of the vents and approaching the levels where noticeable symptoms of exposure begin to manifest. The furnace is only 8 years old and I was not anticipating problems with it (and only had a five year warranty so no joy there, I checked). The repair is 80% of the cost of a new furnace and doesn't make any sense to undertake. This was detected less than 18 hours after fixing the food processor. So it was with some trepidation that I pronounced the TV fixed. It has been about 15 hours since then and I am just positive that something else is about to break today.
I think I need to find at least five or six things that I don't care about that are not currently broken, break them, and see if other problems resolve themselves automatically. Or perhaps I can set up some sort of altar in the utilities room and sacrifice power tools to the dark gods of homeownership. The one-thing-fixed-another-one-breaks vibe going on here is getting creepy.
Well, can't complain too much. Our costs to own so far have been far, far less than the cost of renting an equivalent house by my calculation so even tossing in a new furnace isn't exactly going to make the math ugly, just less pretty, especially since that was not a cost we were expecting. We'll recoup some money on heating savings and a new furnace sure won't make the house sell any more slowly when the time comes. I am honestly more irritated at having to take out the time to solicit bids and meet with contractors than the cost. Also the paranoia about something else breaking is getting pretty strong. I keep expecting the water heater to detonate or the fridge to puke its guts out on the floor. Since we're dealing with paranoia and evil spirits, not rational engineering and probability, I will accept any magical or spiritual help my readers care to donate. In the meantime, I guess I'll just keep working.
*CRT TV's have 30,000+ volt potentials around the tube with more than adequate charge to kill you like a bug zapper. I would never open a CRT. This plasma TV, when unplugged and properly discharged, tops out around 400V with smaller capacitances. Field reports indicate a serious error would leave your arm numb for a couple of hours but generally not kill a healthy adult. I felt no need to be electrocuted and exercised due caution not to ground any of the caps through myself, completing the swap without incident.