How can I tell if a power supply is going belly up?

I'm on my third power supply to an HP Pavilion desktop. I bought the tower as a refurb about 2 years ago. The problems I've had was that it didn't start when I went to power up, so I've been taking it back to the guy I bought it from, and unfortunately, the only local comp repair guy. He charges me about $100 to install a new PS, so I've just been leaving the power on all the time to try to avoid the power surges of turning it on and off. It's been on for a month now, but it's now making a very high-pitched sound. Now I have a few questions - is it better to turn the computer on and off every day or just leave it on all the time and, should I be concerned about the noise coming from the back of my tower (so far it hasn't seemed to affect the system's performance)?