I've fixed this!!
This just happened to me for the first time, my PS3 was fine for years and I've just registered on the Playstation Network, low and behold it's red screened on me!
1. Turn off the switch at the back. Hold the power button down near the red light, the fans will blow a little harder then it will shut down again back to the red power light. Hold power on again and wait for two bleeps then let go of the power button.
2. Press the PS button on your contrroller (it must be connected via the USB charging cable). From the menu select option 3 - Restore file system.
3. Go through the menu prompts. It might make it all the way only to end up as a red screen again, this is frustrating but repeat the above steps. Even try restore system etc (this will wipe any data, my system couldn't even do this without red screening so go back to a file restore if yours is the same).
4. I set my display resolution to 1080i instead of 1080p and it works again perfectly. I'm not sure of the significance of this and I'll change it back to 1080p at a later date now I know how to fix it.
Maybe the cause is a component failing who knows, but it seems to be a software issue as the restore filesystem mentioned an area of corruption that needed repairing.
Either way, it was fine until I joined PSN. Who knows.