It does sound like you may be screwed on the warranty part. Are you inclined to open it up? Yep, there's deadly high voltage to worry about, but you may be able to find the trouble if you want to give it a go.
Has the TV been moved much? It sounds like a loose component in a PC board. Maybe even a loose connector. If you have the back off and power cord plugged in (dangerous), you could try poking here and there till it cuts out. Use a wooden yardstick or something like that. Easy does it, but pry under the corners of the different circuit boards etc. Push on the various connectors. If it cuts out, poke and pry the same area till it fires up again. Eventually you'll find the spot. If it's a loose component you can solder it after the voltage is drained off. If it's a loose connection you can clean that up too. Personally, I'd go for it. Sounds like it's on the way to the shop anyway.
I had an old JVC that did the same thing. We'd have to give it a rap on the side of the case to get it going again. I finally opened it up and found that a heatsink attached to a big power transistor had a bad solder joint. I guess the expansion and contraction of the heatsink worked it loose. Quick dab of solder put it back in business for a few years. Do be careful if you decide to try.