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First, look through the TV's menu for a convergence adjustment. It might be labeled "magic focus" or something similar. If that doesn't fix this or if you don't have that option in the menu, your TV's convergence circuitry has definitely failed. This is probably the most common issue with TVs of this type and age.
You see, your TV has 3 monochrome guns that project their colors (red, green, and blue) onto a mirror… which reflects the image onto the display. The convergence circuit pushes and pulls the colors into alignment so they “converge” at the same point. If the circuit fails, the colors separate like you've described and the picture sometimes warps or bows at the edges.
The circuit is made up of a couple integrated circuits called convergence amplifiers as well as some resistors and pico fuses, typically.
If you’re any good with a soldering iron, you can replace these parts yourself. That would run you $30-$60 typically. If you’d rather not dig into the TV yourself, you’ll need a technician here. Something like this is relatively simple and routine and should run you about $300 depending on where you live.
If you decide to try it yourself, I’d check with these guys first. They have repair "kits" available so you won't have to piece together the individual components. Plus, their kits come with picture-based directions and free phone support. For $30-$60 (depending on your model)… that's a good deal. I suggest calling them... a lot of their kits aren't posted on the site.
If you'd rather hire a technician to do this, check out www.tvrepairman.com and enter your zip code.