1. Have you made sure all video cables are connected fully on the back of your PS3?
2. Do a video reset:
- Put your PS3 into standby mode (until only the red light shows.)
- Hold your finger on the power button until it double beeps the second time (normally 15 seconds).
That should reset your video settings without losing any savedata.
Sometimes that can be the problem.
If none of the above works then get your warranty out and take it back to the store, if you have a launch PS3 its about their time to give in now.
One of my mates just lost his PS3 that way aswell.