As Cody is alluding to is isolation of the problem. Is it a cable issue, an external connector issue, and internal connector issue, a loose or cracked part on one of the circuit boards, etc.
So, Try:
* wiggling the connectors and if that causes the problem to come an go, then try using a different cable or swap them around and see if the problem moves with the cable.
Beyond this point, you'll have to open the TV [].
* if wiggling the cables causes the problem to come and go, but it doesn't seem to be a cable, then perhaps its an external connector. Often the only thing holding connectors in place is solder and PCB traces. These are notorious for cracking. Look for cracked solder around connector pins and re-solder if found.
* if the above didn't get it, then perhaps a cable is loose on an internal connector. With the TV running (you might need to set up a mirror so you an see what's happening on the screen as you do this), try wiggling cables while you watch the screen [again ONLY DO THIS IF YOU KNOW WHAT THE HECK YOU'RE DOING SO YOU DON'T ELECTROCUTE YOUR SELF -- though these newer LCD TVs are probably far less dangerous than the old CRT TVs with their 20-30KV line -- I've only worked on CRT TVs--long ago). If one of the cables causes the problem to come and go, then see if it needs tightening or needs to be reseated, and again, look for bad solder joints.
* Otherwise you probably have to put a scope on it, and see if you can get a Sams Photofact on it, or something.
Also, this should go without saying, but opening up an LCD TV can likely lead to all kinds of other grief if you don't know what you're doing: broken wires that you have no idea where they go. Parts that fall out, and you can't find where it/they go, wires, circuit boards, etc. that won't go back into the case--stuff like that! So, good luck!!