Geek of the week? Heck im always that!! And yeah the LCD tv's show up free all the time, and if you got a little time on your hands there is good money to make off them. I generally pick up dead units off craigslist for nothing or a few bucks, put $20-$30 worth of
parts into them and sell for a couple hundred depending on size and age.
In your last post the second picture of the board with the blue transformers is the power supply board. The other two boards are the inverter boards, and the blue board with all the connections is of course the mainboard. The two large fat caps are the primary side and they rarely fail, but suspect all the small brown caps on that board as they are likely Elite brand capacitors. Sony and RCA had a HUGE problem with their manufacturing using Elite branded caps. Very cheaply made chinese caps that fail after a year or two tops. The primary caps you will notice are Rubycon, they spent the big bucks there and then cheaped out on the secondary side with the Elite caps.
Look for any caps that bulging on the tops, sometimes they bulge on the bottom too if they were not tightly installed against the board, the pressure goes out one end or the other. Also sometimes you will not even be able to visually see anything wrong, but they are still bad. On that power supply board did they silkscreen the voltages or anything on there? The two multi conductor plugs at the bottom right of that picture is where you should see all the voltages, 5v, 12v, 15v, 24v to the backlight inverter, the voltages vary by model but generally you have 5v, 12v, 24v. Check them with a voltmeter, put the meter on the line turn the tv on, watch that voltage, you will probably notice one of the rails are kinda low, usually on Sony and RCA tv's the 5v supply fails under load and the voltage drops too low which makes the logic on the mainboard reboot the tv in an attempt to clear the problem itself.
I can tell you one thing for sure, its the power supply board or the mainboard... LOL I know it doesn't help right? Lots of troubleshooting, i generally start with the power supply and check voltages and go from there.