My Sony CCD-TR81 camera tries to focus but can't. It makes a clicking sound.

I have got the same issue. It sounds like when a motor goes past a point and can't go no further. I don't know anything about cameras and there internal workings, but when you extend the focus ring all the way our and turn the camer on, the camera will not make that noise until the focus ring is back to it's full in position....

Sounds like the CCD is damaged. Sony was fixing this problem free of charge but has since discontinued the free repair. If your camera was exposed to excessive heat, such as in a car during the summer, the CCD could be damaged from an iodine vapor within the camera itself.

Here's a website that has a few photos showing some distorted images from a bad CCD.

http://www.imaging-resource.com/badccds.html

The Sony websites that listed information regarding the free repair are no longer available.

I know this doesn't help your situation but if you can obtain a new CCD from Sony parts or similar, there's a YouTube video showing someone replacing one in under 10 minutes.

http://www.youtube.com/watch?v=rnZdEc9KY-U

Seems your DSC-T1 camera got bad cd imager problem and Sony will repair it free of cost.
Click Sony CCD Imager Support for details.

This sounds like a description of one symptom of a failure with a ccd imager chip that I just received from Welcomejee. Reading the document at the below link describes a black screen, a test you can use to see if that's the problem, and if so, you can mail the camera to Sony for a free repair. Here is Welcomejee's response:
"It is failure of ccd imager chip in your Sony DSC-T1 camera and Sony will repair it free of cost.
Click Sony CCD Imager Support for details."

Its's problem of ccd imager in your DSC-T1 camera and that part will be replaced.
Sony announced free of cost repair for subject problem. Click Sony CCD Support for details.

PS. Mine had the same problem, and I mailed it to Sony. They replaced it free of charge including shipping cost. BE QUICK! The free replacement ends in March.

Its known problem of ccd imager in DSC-T1 and can be fixed by replacing ccd imager.

Sony will repair it free of cost as per announced scheme of ccd imager problem in this model.

Click Sony CCD Support UK for details.

http://www.henrys.com/manuals/sony/CCD-TR818(en).pdf here is a link to an online manual that i used awhile back, hope this helps.

CCD Imager is defective in your camera and need to replaced.
Sony announced free of cost repair scheme for such problem in DSC-T1 and you can have this facility by clicking Sony CCD Support.

Sounds like you have two problems, both which mean bad news. The clicking could be a broken gear in the lens unit or off track lens.
The colors may be caused from a bad ccd or sensor internally.

Not much that you can do with that, try adjusting the small focus lever on the underside of the viewfinder, as this might fix the blurred image, your lucky that you didn't, break something on the camera.