Instructions
Verify that the PS3 is plugged into a working AC outlet. If the AC outlet has an on/off switch, check to see that the switch is turned on.
Confirm that the AC cable is plugged into the back of the PS3 fully and securely. Some pressure is required to fully insert the AC cable. While connecting the AC cable, check the condition of the cable. If the cable is cut or looks damaged, it may prevent the PS3 from powering on or damage the console if it does power on.
Check the air vents on the back and side of the PS3. Dust and other objects blocking the vents can cause the PS3 to overheat and not power on.