Great news! I yanked the chassis, and found a jumper that had been corroded down to a thin filament. Also found some spongy green scuz that, if conductive, was shorting two wires together. I buzzed out all the board to board connections with a low-current ohmmeter and found them to be in good shape. I checked several vias on the double-sided board and found those all to be fine as well. I wonder if some of what appeared to be a large area of previously-wet board was something left over from manufacturing, perhaps a final cleaning process. The real problem turned out to be on the center single-sided board in this area right behind the "jungle" plug-in board:

I cleaned up that green stuff and replaced the severely corroded jumper (obscured by the jungle board in this image). I slapped the chassis back into the set and it fired up and it is working fine. Now I've go to get some vinyl siding to make a drip tray.
I'm glad I didn't have to buy a new TV. I was out looking at LCD and plasma HD TVs this past week and was not impressed with what I saw. The high-speed update that these new screens have really brings out the "blocky" encoding artifacts in the MPEG images, particularly at scene changes and in scenes with a lot of motion in them. There is some new technology just now appearing in very high-end screens that cleans up a lot of those artifacts. I hope the old Mitsubishi can hang on for a couple more years until that post-processing technology makes its way into the mid-range (~$2,000) 47" screens.
Leonard, thanks for your advice. You saved me a bundle of money. Can I mail you a beer?
Thanks,
Jim