Computer making sound when turned off

"My money's on a bad power supply.

Power supplies are transformers, and they can make a very high pitched (I hear it as almost a hissing sound) noise, especially when they are failing/failed. In this case, it sounds like the power supply has given up the ghost and now makes noise, as you say, 'like a TV set'.

As to why this happens, I have no idea. I suppose this could be oscillation of a hardware component, or something. One message board says this about televisions:

As CRT TV's get older, the laminations in the coils get dryer and looser. allowing the coils to vibrate. This acts as an acoustic amplifier for subharmonics of the frequency the circuit that the coil is in operates at.""

But I have heard the same noise on computers and very shortly thereafter, they are dead."

"Where is the origin of the sound? If it's through the speakers, yes, could be interference.

If it's not, it could well be the power supply. They can emit a high-pitched whine when they're dead/dying.

Check your graphics card. If your card is fried, the machine may not post."