First test to see if it's your monitor and not something else that's causing the hang. Set it to not have your monitor sleep (if it's a CRT monitor make sure to set a screensaver as well to prevent burn-in). Leave it inactive for a good while and check it. If your PC is responsive after a long time of inactivity, it's certainly something to do with video or the monitor.
You may also want to check in advanced settings for your power options if your HD is set to turn off after a while, as that is often the reason for PCs freezing while inactive.