I had this exact same problem with the same model of 27 inch JVC (Model AV-2751S). Someone had put this TV at the curb to be thrown away and I took it home and after running it for awhile the video started tearing and a narrow white horizontal line was all that appeared through the center of the screen. After unplugging and removing the back I discharged the picture tube and took off the wire connectors to the circuit board. After sliding the circuit board out I cleaned the bottom of the board with 99 percent alcohol with a cut down paint brush. I touched up the solder connections on IC421 and the other IC chips. After cleaning the collected dust and dirt out with a vacuum and using an anti-static spray of my own concoction (scent free fabric softener mixed with water in a spray bottle) on the plastic case, wiped dry, I reassembled the chassis and the TV now works perfectly.
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