If you have other equipment connected to the tv try to remove then, plug only the tv using the RG6 or what ever cable you are using for the antenna. if you listen to sound and continue with green screen most probarly their is a problem With the tv. by using the tv antenna you eliminate any problem in the component or composite video of your tv.
If you are using a digital converter box and composite video cables, as mentioned before, check that all of your cables are seated correctly.
I had a problem with faces turning green, and it turned out to be a loose cable from the converter box.
PatM
depending on model and powersupply fitted,check for hi esr electrolytics-you may find some heat sensitive in which case a short localised spray of freezer will help find the faulty component(s)
also if you have an isolation transformer and a scope -connect yr lcd via the isolation transformer to the mains and check all the seconday supplies from the smps for ripple when the set s in the fault condition.....