It sounds like your PS3 has suffered from a hardware failure, if I'm reading what you're saying correctly. Does a yellow light flash before it turns back to red?
Search about YLOD In google , is that your problem ?
EricIs the power supply external on the slim model PS3s?
It's a fat ps3 btw
Have you tried a different power socket, a different cable? It might be that your PSU has gone which is a pretty inexpensive fix. You could also try opening it up and replacing the thermal paste on the chips as it might be overheating.
What psu