My computer will freeze, seems like a lot of folks are having this problem, and my only recourse is to hit and hold the off button. Sometimes it will start right back up, while other times it may take 5 to 15 starts. Most of the time I have to wait a few hours before I get any success. I've notice that when the computer starts and if the small motherboard fan starts up, everything will work fine. I've cleaned out the computer, no change. Any advice would be appreciated.

Have you checked to see if the mother board fan connection is loose or if it isn't running consistently and it needs to replaced? In my experience a broken fan will cause the computer to overheat and lock up. Perhaps the reason it takes a while before it will come back on is that it is cooling down with room temperature. I had a similar problem a while ago and replaced the fan and all was well from that point on.

The fan connection is good, I'll try to replace it. Thanks.

jeffp is correct. Most motherboards watch the CPU temperature, CPU fan's speed, or both. If it falls outside a preset range, (causing a temperature rise) the system determines the fan must not be pushing enough air to cool the CPU, so the system shuts down, or halts to prevent damage to the CPU. Just dying or locking up isn't a nice way to do it, but at least it save the expensive CPU.