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Since all your inputs are affected, it's safe to say the TV has an internal failure at this point, and things like this are definitely reparable. It will just boil down to cost, so the real question is: Will this be cost effective? The answer is... probably not. It would be a wiser investment, to replace the TV. It's tough to say for sure what's causing this without getting inside the TV, and although some hands on diagnostics wouldn't run you more than $50-$75 (in my area), the final repair bill would run $250-$350 depending on the results of the diagnostics.
So, what could be causing this? Things like this can be caused by a couple different things. More specifically... the power supply board, or the main board are our main suspects here. Based on the age and original price of this TV, however, I doubt either of these would be cost effective to replace.
If you do have it looked at, feel free to post back here with the technician's findings and the repair estimate. I'd be happy to let you know what I think. Otherwise, it might be time to replace the TV.