My computer freezes, then won't start up

[JTG51]

Maybe once or twice a day while I'm in the middle of doing whatever I'm doing my computer completely freezes up so I have to hold in the power button to turn it off. Then when I try to turn it back on, a lot of the time it sounds like one of the fans is going much faster than normal, but it won't start up. There's power, but nothing happens. Sometimes I have to turn it off and back on several times before it works.

This is a fairly new problem. As far as I know, I didn't make any hardware or software changes before it started. I hasve noticed that Zone Alarm sometimes takes quite a while to start when the computer starts up and the system is super sluggish until ZA does start. Is there any chance that's causing a problem?

Any idea what's going on or how I can fix it?

Thanks.