mmm unseated RAM would cause more blatant issues, like sometimes the computer not posting, or getting blue screens.
What are the specs on the computer. What operating system are you running? If its a Pentium 3 with 128mb of RAM id say that would be your problem right there. 5+ year old hardware wasn't designed to run a modern day operating system (Even XP SP3 way too much for that).
But if its not that old, freezing could be due to a bad driver, bad RAM, bad hard drive.
Next time you have the computer up and running right click on the My Computer and go to manage. Check the windows log for any errors. Most errors can be ignored, but look for disk errors, memory faults.
Next to test the hardware you may need to bring it to professionals. But I know us forum people are too good to bring it to geek squad/firedog, but they have the tools to test these things. But for home use I can give you a few suggestions.
Hiren's Boot CD:
http://www.hirensbootcd.net/
Download it and burn it to a CD (on another computer preferably).
Next boot to the CD (much like you would a windows XP CD), Go to testing tools, and select PC Doctor 2004; From there run a hard drive test. If it comes back with any bad sectors then there is your answer, you need a new hard drive. Take it to your local computer shop and have them clone your failing drive to a new one.
Next if your hard drive passed all of its tests then look at RAM, reboot the computer and boot to hiren's boot CD again. This time go to testing tools, and select memory tests and run a memtest 2.26+ (I forget the version), let it do a few passes, if you get any red, well you have bad RAM.
Try updating drivers, every driver even printer ones. Sometimes an outdated / corrupt driver can cause issues like this. You can download them from the manufacture's web site.
If your still having the issue, then its the operating system. I know you said you reinstalled the OS, but are you installing it from a recovery partition? The recovery partition could be corrupt, reinstall from fresh media (aka: CDs / DVDs with windows on it), then download the latest drivers from the internet and go from there.
BTW I do this for my job while I pay for school. I know what im doing ;P