High pitched squealing is usually the sign of imminent hardware failure, and is usually a PWM on the motherboard or CPU. If you can isolate the sound's location (PSU or mobo, or elsewhere) you can help figure out what part is bad. If the system is having problems locking up though, it's a very telling sign. In about 90% of the cases like this one, it's a bad power supply (or overloaded, or a failing unit) and replacing the PSU will often fix the noise and locking issue. However if the noise is coming from the motherboard, well, you guessed it, time for a new mobo.
Edit: I was typing when you replied zack, so if you've isolated it to the PSU, definitely get a different one (though in all seriousness, the good power supplies are generally heavy - if you can lift one up with your hand and it feels really light - you'll know what I mean - then put it down and get a different one)