Thanks for choosing JustAnswer for your TV question!
missing parts of the picture, especially half the screen or in blocks as you describe , Is usualy a flaky buffer. The buffers seperate the picture into "zones" each of which is controlled by a buffer (or drive board). It can only be diagnosed in person by a technician, anything else is basically guesswork.
From the sound of your problem you should probably call for service. There are too many variables involved to diagnose a problem such as yours over the internet. Modern TV's have thousands of parts, it can take a seasoned veteran up to an entire day to track down troublesome problems IN PERSON.
Please understand that by opening a TV you are exposing youself to many dangers, including electrocution. Be sure that the set is un-plugged and keep one hand behind your back whenever possible to avoid a shock through the heart as this CAN KILL YOU. If you have zero electronic experience I would not attemp this repair. OK, public service announcement over.
Basic electrical knowledge is a must to get inside your TV and fix it.
Your TV will need some parts and it is best to either leave it to a technician to diagnose.
If you call for service prepare to part with $200-$450 depending on the damage in the TV.
You can call Your manufacturers customer support at the phone number in your manual to find a local repair center. They do this for free so you can get your set repaired.
Wish I could be of some more help to you.
Hope that helps!
If you feel my answer was satisfactory please click on the green "ACCEPT" Icon, the question will not close, and you may follow up if needed. Thats the only way I get paid for my advice.
Feedback is always appreciated!