Lg is flickering and has double image at top of screen only

try changing picture size

Clean the cable and connector contacts for starters, if that doesn't solve your issue try a new tcon board.

Forget the repair, replace it.

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Looks like either a TCON board failure or if you are lucky it could be a flex cable connection problem at the TCON or Main board.

If you can hear sound, then screen is gone.

I'll bet you don't.

If you see an image, hear sound, just won't hold.
I'd bet on the T-Con board.

Not knowing what is really happening here..

If willing to dive into electronic's.
Open her up and start testing power side, starting with capacitors.

you have answered your own question: you have a loose plug or other connection somewhere in the set--not a do it yourself repair and if LG I would call them to see if this is a known issue in this model.

It could be any of 4 boards, either take it in for service or get a new set.

From my experiences working with projectors, more than likely you will need to replace the lamp