When air or heat comes on the tv screen appears to lose connection

Start simple by using different cables, whether they be HDMI, VGA or standard COAX cables. They could be losing the connection. Also, it's possible the power supply is wearing out and it gets too hot. You might want to simply try some spray air duster type thing to clear out any dust that can make it hot.

This problem can be caused by a lose connection between LCD and motherboard, however you can check it by opening the LCD or hinge bezel to ensure if there isn't any lose connection.

t con board on the back of the screen will need replacing, its the one with the wires going to it from the main av board to the screen. the chip can become damaged due to heat or even come away from the board. if its working when you bag the board it could be a lose connector or the connections that is soldered to the board have come away and will need soldering back on.

there is a dtv board inside. you may need to change the board or it may just not be connecting properly clean the connector and see if it works then they can come lose when tv is move about.

If you have a rear projection LCD TV the cause is excessive heat, that in turn is normally caused by dirty air filters or poor air flow.
If you clean the air filters out it may halt the progress of the problem.

The solder connections at the vertical output integrated circuit are bad and losing contact as the part heats up. A few minutes with a soldering iron to repair the connections should fix that up.

It sounds like your TV/monitor is losing the video feed. That's why it displays 'Video' - the label assigned to the input - so you'll know the TV is turned on but missing the input. You would get the same response from the TV if you turned the DVD off. I'd look at the integrity of the video connection from the DVD.

Bad connection somewhere along the bottom or top of the panel, there are boards most likely along the bottom of the screen that control vertical drawing, a connection that breaks as it is heated up sounds about right. check the connectors along the bottom. Be very careful because if you wreck em the screen is junk. The connector that will be at fault will be in direct line with the black bar.

check the convergence area for bad solder
http://home.earthlink.net/~oleg.filippov/ConvergenceFix.htm
http://cmpalmer.blogspot.com/2006/11/fixing-my-own-tv-part-ii.html
Sony Convergence
http://www.techlore.com/blog/entry/19694/Sony-Convergence-Repair-My-Sony-TV-has-a-distorted-picture-/
http://www.techlore.com/article/19631/Sony-Convergence-Procedure/

It sure sounds like you have a classic case of bad solder joints. Resolder all the connections on all boards.