The fact that it clicks then shuts itself off. would indicate that there is a short inside the set stopping it from fully powering up.
It is most probable that there is a failure on the power supply board inside the TV. Commonly the capacitors on this board will receive a surge and then fail.
They can sometimes be visually verified by removing the rear of the set and inspecting them for bulges or leaking fluid at the top or the base of the caps. This is the most common mode of failure for these sets.
The capacitors are located on the power board inside the set, where the AC cord plugs into and can be replaced by a Tech for no more than $150 parts and labor if this is the case. The power board itself will run you roughly between $300-$400 to have replaced.
Unfortunately there is no sequence of buttons or reset you can perform to get the set working again.
Do you have any experience testing live voltages, or soldering on electronic equipment?
If not, then I would suggest using the link below to locate a technician in your area:
If you need further assistance, let me know.