My screen fades to red, then the TV shuts off

It is your red picture tube that is your problem . This is common with Sony projection TV's of your age . You will need to replace the picture tube . If your going to do this yourself you should have some knowledge of replacing a picture tube as you need to align the yoke and purity rings and adjust the settings of the red tube. If not call around to some local shops not the big box stores to get the best price on labor and parts . Depending on the price of the tube expect anywhere between $350.00 to $500.00 to get fixed . There might be a remote chance of a loose connection on the red circuit board and this should drop the repair price $175.00 depending on there labor charge . Make sure your colors were very good before you had this problem. If not all three need to be replaced and this would be costly and cheaper to buy a new TV. So if a shop tells you to replace all three this is only done if your colors were weak and the picture was not as bright and clear . Good luck , Team tech