This problem can happen due to several things. The power supply is a common cause of this problem. This typically will cost you $250-$300 to have repaired.
The other very common issues, are problems with the Sustain boards failing. They are responsible processing the Plasma display and are common failures for this type of TV. The average cost for this type of repair is around $350 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.
Given the age of the set it may or may not be more cost effective to put that same money towards a new LED TV, in lieu of repairing this one.
However if you'd like to inquire about repairs, or seek a 2nd opinion, you can use the link below to locate a shop in your area:
If you need further assistance let me know. Before you go, PLEASE DO click at least a 3 STAR RATING, at the top of your screen. That is how I am credited for my efforts by the site. You can follow up any time as needed at no additional cost.