There is a 4 inch wide line across our 51 inch plasma tv. is it fixable

SOURCE: philips plasma tv vertical black stripe

Check these videos for repair instructions for black lines.

Just requires some soldering.

Video 1 / Part 1
http://www.youtube.com/watch?v=9NPobj0_GSo
Video 1 / Part 2
http://www.youtube.com/watch?v=ITd6Ahdi4s0
Video 2
http://www.youtube.com/watch?v=qBpg77ZzFFk

SOURCE: LG flat panel plasma with red line

I had the same problem and fixed it by replacing the control board. It's a little nerve wracking, but required only simple hand tools. If you'd like to see detailed pictures of the repair check out my blog.

http://greenrenovation.wordpress.com/du-42px12xc-repair/

SOURCE: nec plasma tv 42MP4

these plasma vertical black lines are notorious. there's a video of a fix on this plasma tv repair site. good luck!

SOURCE: Black line on Panasonic Plasma

go here and follow, it will work!
http://www.avforums.com/forums/plasma-televisions/462873-black-line-fault-hyundai-hpt4240-fixed.html

enjoy!
stephen

SOURCE: Permanent Vertical Line on my Sony Bravia 46 inch LCD TV

What you're describing is usually the result of an improperly seated connector. With the power disconnected, open the tv and locate any connectors between the LCD screen and the driver circuit board. Unplug them, and reconnect it assuring it's properly and firmly seated. Be careful when handling these cables as they tend to be quite fragile... take your time.