Check to make sure that power outlet is still good... sometimes they fail. Or, split outlets might have a switch running one part of the outlet (like to a lamp), so check both receptacles. So, try another outlet.
Make sure you're trying to turn it on via the switch on the TV itself... I've seen a person forget that batteries die in remotes, too.
If not, the power supply board inside the TV may be dead - no "clicking" noise usually means zero power to begin with.
Any nasty smells lately to suggest a board burned out? It's pretty unmistakeable when they go.
If you can see inside to see if there's a blackened board, fuse, etc. then that'll give you something to go on.
First checks though... it's either a burned power board or outlet... less likely the outlet. Yup, power outages and the sudden spikes when power comes back on can fry poor TV's and computers.