When your PlayStation 3 refuses to shut down, it's usually a software hiccup or a minor hardware issue rather than a catastrophic failure. Follow these steps in order—from simplest to most involved—to get your console powering down properly again.
Press and hold the front power button for at least 10 seconds. You'll hear one beep when you first press it, then two quick beeps, and finally a third beep signaling a forced shutdown. Release the button after the third beep. This cuts power to the system immediately and resolves most temporary freezes.
If you use a Bluetooth remote, a PlayStation Portable via Remote Play, or a third-party controller, one of them might be sending a constant "on" signal. Remove the batteries from any remotes, turn off the PSP, and unplug USB peripherals. Then try shutting down again.
Navigate to Settings > Power Save Settings and turn off the following:
A disc stuck in the motor can block the shutdown sequence. Try ejecting the disc normally via the Game column in the XMB. If that fails, hold the Eject button for 10 seconds to force a mechanical eject. Remove any disc and test shutdown again.
If the fan is screaming or the console feels excessively hot, thermal protection may be preventing a clean power-off. Power off via the forced method above, unplug the unit, and let it cool for 30 minutes. Clean the intake and exhaust vents with compressed air. Ensure the console has at least six inches of clearance on all sides.
The PS3 uses a standard figure-8 (C7) AC cable. Swap it with a known-good cable from another device (like a laptop charger or another console) to rule out a faulty power connection.
If the console turns on but won't turn off, boot into Safe Mode:
Unplug the AC cord from the wall outlet. Wait five full minutes. This drains residual capacitance from the power supply. Replug and attempt a normal shutdown. If the problem persists, the power supply unit or motherboard likely has a hardware fault—consult a professional repair service.