The first thing to check is if your power outlets have surge protector breakers. Try plugging in another simple appliance like a lamp into the outlet and make sure the outlet has power.
If the outlet is fine try plugging in the TV and listening very carefully from the back of the TV for a subtle click noise. The power supply has a mechanical relay that switches when the TV receives power. If you can not hear the click and there are no stand by or power lights illuminated then you likely have a power supply problem. This could range from a blown fuse to a bad capacitor up to a burnt out power regulator. Anything more serious than those problems may warrant simply replacing the whole power supply. Depending on your TV that board could cost anywhere from $50-$175. The power supply can be tested using a multimeter to determine if it is the source of the problem but this should not be attempted unless you have some electroics repair training and are aware of the dangers involved in working on high voltage electronics.