So the good news is that I found a model (PN50C450B1DXZA) of the approximate time period, and I just went with the 720p. But it's the same series, so that ought to be close enough to make a reasonable guess.
That bad news is that this is service issue.
Also, since you originally asked, the short answer of "what's going" on is that it's a power system issue, which needs to be serviced.
The longer answer of "what's going" is that the TV has a protection system built in to prevent elements from drawing to much power a destroying themselves. So somehow too much power is flowing through that safety system, and like a breaker box, it shuts itself off to prevent damage. But I'm not going to speculate what portion of the electrical system is the cause, because you need someone there looking at it to figure it out.
So if you want someone to service it, then you can go to this thread here for instructions on how to set that up: http://forums.cnet.com/7723-13973_102-542437/service-issues-click-here-for-help/
Hope this was too disappointing for you. Have a fantastic day!
-- HD Tech