We have a 56 inch JVC HD-56G786 backlit projector TV and the screen just completely pixelated while watching cable. I turned it off and back on and now even it has a green screen with staticy vertical lines whether the cable is on or off. Any idea what the issue is?

Possibly your digital tuning PCB

part#: SSD-2104A-M2 $82.00 http://www.shopjimmy.com/catalogsearch/result/?q=SSD-2104A-M2

or your Audio PCB (includes tuner)
part# SRP0R021A-M2 $120.00 http://www.mcmelectronics.com/product/JVC-SRP0R021A-M2-/SRP0R021A-M2

$42.45 http://www.ebay.com/itm/JVC-HD-52G886-Audio-Board-SRP0R021A-M2-/111366506848?pt=US_TV_Boards_Parts_Components

$119.59 https://www.encompassparts.com/item/6195501/JVC/SRP0R021A-M2/P.w.board_Assy

'Goggle', "JVC HD-56G786" and pick one

NO!
http://www.shopjimmy.com/dlplamps?tv_brands_select=Jvc&tv_models=Jvc+HD-56G786

have you ever went thru your hdmi setup procedure that jvc recommends?

Here is the manual for your tv. On page 51 it will tell you how to turn on and off the CC.

http://server4.nodevice.com/downloads/4e1fdaec439e1d8864e7377154b583f4/hd-52g786.pdf


Good Luck and Please Rate FixYa!

i would take it to a shop and have them repair it so its done right.they can be funny the way they act but they are normally good tvs id take it in for repair

I would suggest, since you have some technical background, that you download the manual for your set.
This site seems to have the best prices of any around:
JVC HD-56G786 Service Manual 

It would be interesting to know what the $600 got you.
Many of these kinds of failures are attributable to power supply problems and depending on the design of the supply and knowledge of the repair tech, it may be a repetitive problem.
The only way to fix this permanently is via the detailed inspection of the circuit, replacement of the failed parts and often, the addition of certain components to provide some protection of the parts that will likely fail again. Replacing of the supply completely will probably only give you momentary relief until these parts (almost surely chemical (electrolytic) capacitors) before they again fail to perform their designated function.  

kinda like a water mark... i fixed a few of these and to me it sounds like something in the optics. eather on the mirror or in the engine... send it to a shop while its still under warrenty. they probally will replace the engine for you under warrenty.

can you see lines over your menus? if so, replace light engine.