Thanks for the reply Bob, and unfortunately nobody can give you an answer based on the symptoms you have alone.
This problem can happen due to several things, and to determine which, a Technician would need to first inspect the Power Supply Board for signs of faulty Capacitors, as well as measure the voltages coming from the Power Supply.
The Power Supply is one of the most common causes of this problem. The capacitors on this board can swell and bulge due to receiving a surge, and can cause a voltage drop on one of the outputs on the PS. This typically will cost you $250 to have repaired.
The Mainboard, which carries the turn on signal to the power supply can also cause the Power Supply relay to click. If the Mainboard's signal is glitched due to a fault on the board, this problem can also happen. Average cost to have the mainboard replaced is around $275 parts and labor.
The other very common issues, are problems with the Sustain boards failing. They are responsible for producing the image on the Plasma display and are the HARDEST working boards in the set. They also incur the greatest amount of heat which can cause failures such as the one you are having. common failures for this type of TV. Average cost for this type of repair is around $450 parts and labor.
I wish I had better news, but the set will require component level testing and replacement in order to function properly again.
If you'd like, you can locate a tech using the link below:
If you need further assistance, let me know.