It certainly sounds like a CCD sensor problem.
I suggest you phone Canon support and tell them the problem and that you suspect the CCD.
Ask for a repair quote for a CCD replacement.
After you get a quote, you will have a better idea about repair or buying a new camera.
I've had my Powershot A610 (swivel LCD) for a little less than a year and half. It hasn't had any major problems, except for an E18 error last August from a lens that wouldn't retract, which was fixed by Canon and covered by my warranty.
Starting a little while ago, I would power up my camera and the screen would be black. All the icons were still visible, and I was able to take a picture, but when I switched over the mode to view the picture, it too was all black. However, after taking one or two of these "black" pictures, the camera would return to normal and function as it always had.
Today, I turned on my camera and the screen was black. However, even after taking HUNDREDS of blank photos, the LCD is still black (still, icons and the blue "Canon" logo appear at startup). I went onto the Canon website and typed in my serial number, etc. and was informed that the repair would be at least $107 plus applicable taxes and shipping (I'm not under warranty anymore), but of course that quote might go up once they receive the camera. I've read online that dead CCD repairs can be quite costly, but I don't really know.
What I'm really wondering is the rough estimate for the repair of my camera. I would send it to Canon and wait to receive the final quote, but I do need a camera in about 3 weeks. I was kind of hoping to purchase a smaller model, like an SD600 or SD1000 anyway, and if the repair is going to be substantially more than the original Canon quote, I'd prefer to just purchase a new camera now. I found an SD1000 for only $260 at Circuit City, so any repair costing more than $150 doesn't seem too worthwile to me at this point.
Also, by no means am I a camera expert. Based on my research I think the problem could be a dead LCD or CCD, but I really have no idea. I'm pretty sure that I've covered all the possible troubleshooting options (new batteries, switching shooting modes, pressing the display button), but any suggestions would be welcome.