I bought a Sharp Aquos 32" TV just over a year ago and recently the picture goes off but the sound remains, this normally happens when changing channels with Sky but it somestimes just happens in the middle of watching a program. I've googled the problems and seen quite a lot of people with the same problem but no solution and now the TV is out of warranty. Sharp support have been less than useless!
Sounds like one of three things:
1) Mainboard/Tuner problems - although I'm really only saying this because you guys seem to think its associated with your over the air channels.
2) Power board problems. You power board/inverter may be damaged in some way - blown capacitor or other malfunctions. This is very possible as this could result in the backlight turning off and the screen going black but keeping the keeping the sound. If this is the problem, it will at some time start to happen constantly. Have a pro open it up and look at the power board.
3) The backlight is defective/dying. The backlight is a set of lights that reflects through the LCD panel. If the screen looks black, but you might see a faint picture or you still hear sound, then the backlight is not on. The panel itself could be defective. You can fix it by replacing the whole LCD panel (expensive), replacing the backlight panel itself (need a busted LCD of the same size with a working backlight), or fix the backlight, which is tough and risky.
Most likely its either the power board or backlight. Either way, you need someone to open up the TV and take a look inside. Good luck! Hope it works out.