Hi there and welcome to Just Answer. Thanks for asking your question.
Unfortunately you have a convergence board problem. This is very very common in older projection TVs like yours - maybe the #1 problem.
The TV has three color tubes in the lower half of the cabinet that project an image off the main mirror and onto the back of the screen. The convergence board processes the signals to the tubes and adjusts the light beams so that the red, blue and green images all line up. When the board fails, the light beams don't line up and you get the '3D' image with the separated colors.
The board has two main components called convergence amplifiers (some call them STKs or convergence ICs). They can fail. It is also common for some pico fuses or fusible resistors on the board to pop. If all three colors are off, then the STKs are probably bad. If only one color is off, then it could just be a pico fuse.
Some people fix the board themselves but it is not a job for a beginner. The parts are only about $60 but you need to know what you are doing. I can point you in the right direction but you need to have a good understanding of soldering and troubleshooting basic electronic components. You would also need to pony up for a service manual.
To have it repaired will cost you about $300-$400 depending on which model Sony TV you have.
I'm sorry it isn't the best news.
I will be here if you have a follow up comment or question.
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