We have a 32" LG television, and turning it off gives us problems?

We've owned an LG TV (Model #: 32L630-UD) for about three years now, and it's been giving us problems after we turn it off. After turning it off, by mistake maybe, it doesn't come back on for around four hours. The red light at the bottom right of the TV turns blue, so it certainly thinks it's working. Not too much more than the really happens. Thanks for the help.

My Samsung TV (model TXH2556) is several years old and has been fiine until yesterday: it opened up with a half picture, on the bottom only, with a bright white line separating the black screen on top from the bottom picture. HELP!!