illastic,
When your computer freezes does your mouse cursor lock up too? If so, then the main culprits are heat or insufficient power/
PSU dying. Since removing the USB drive doesn't seem to help, you may be dealing with a heat issue, make sure that all exhaust fans (
CPU Case fans and
PSU Fans) are clean and dust free. Another good test would be to remove both side panels from your tower and run a standard oscillating fan through it. If that fixes the problem then we've narrowed it down.
If none of that works you could also try downloading the trial of drivesitter to run diagnostics on your hard drives to make sure that your 300GB isn't starting to flake out on you.