I'm afraid I know what’s wrong, and it's not good news.
What I'm pretty sure you have is a defect developing in the panel, which is the actual screen.
When the problem is happening, does it change from one input to another? I'll bet it doesn't.
If you change picture sizes does the problem change? Again, I'll bet it doesn't.
If you press the TV's MENU button (may be the HOME button on your set) to get the Sony on screen menu, does the problem interfere with the menu graphics? I'll bet it does.
If that's the case, it's the screen.
Unless this is under warranty, this is going to be a major expense to fix, and is precisely why I urge anyone who buys a current technology HDTV to get an extended warranty. All of these TV's, regardless of whether it's plasma, LCD, or rear projection, have large and expensive assemblies that cannot be fixed, and must be replaced.
But I would definitely try contacting a Sony authorized service provider and see what they say. They take these on a case by case basis, and may either fix the TV or give you a substantial discount on a new TV so definitely contact Sony Technical Support.
Sorry for the bad news.
Let me know if there's anything else I can do for you, and thanks for using JustAnswer!