Update--
I found a repair shop in my area, and took it in. The "repair shop", as I came to find out, is actually a retired guy who has a small shop set up off of his garage. I had him do his diagnosis--$60 fee, paid up-front. The next day, he called me back, and said that he's pretty sure he has it isolated. If I would give him the go-ahead, he'd make the repair that he thought it was, and if it worked, it would involve about $70 in parts and about $100 in labor. (The $60 I already paid could apply to that, so I'd only owe about $110 more.) If it turned out that it wasn't that, then it would be a situation where it wasn't worth the repair costs. In that case, he'd take his parts back out, and I'd still only be out the $60 diagnosis fee.
I agreed, and it turned out that his fix worked--the TV is back running fine now. Considering what it would have cost for me to get a new one, I'm glad I had it repaired! Thanks everyone!