If it isn't the hard drive (which it may be), it could be RAM at fault. There's a free tool which tests your memory, although it is a bit more complex to use than HD Tune. You have to burn a file to a CD as a bootable CD in order to use it. Here's a step-by-step:
1. Go to
http://www.memtest.org/#downiso
2. Look under "** Memtest86+ V2.01 (21/02/2008) **" for a link labeled "Download - Pre-Compiled Bootable ISO (.zip)"
3. Save the file it links to and extract the compressed zipped folder
4. You'll get a file ending in .iso as output of the decompression; if you know how to burn a bootable ISO CD then do that and skip step five
5. If you don't know how to burn a bootable CD from an ISO file then head to
http://isorecorder.alexfeinman.com/isorecorder.htm
-- Download the appropriate version; probably the 32-bit version one the page linked with "ISORecorder V2 - for Windows XP SP2 and Windows 2003"
-- As I suspect you have Windows XP, Service Pack 2 32-bit, this is a direct link to the installer:
http://isorecorder.alexfeinman.com/download/ISORecorderV2RC1.msi
-- Once installed you will be able to right-click on the downloaded ISO file and see an option for "Copy image to CD"; click that and follow the instructions to burn a CD with memtest on it - obviously you'll need a black CD in your CD burner
6. Once the CD is all prepared insert it in your CD drive and restart your computer. You *should* boot into the CD (or be given an option to) and, once in it, will be given options to run tests. Let the tests run repeatedly for a few hours; if any errors appear you've got a problem.
If the CD doesn't boot automatically then we have to fiddle in your BIOS settings to get it to boot. I can attempt to direct with that, although it is difficult without seeing it. Use Viper's idea first; it requires but an install. Don't waste time on this unless HD Tune doesn't show any problems.