Computer Randomly Freezes

I have a computer at home that is experiencing what are (to me) some strange symptoms. Whenever the computer is being used it sometimes randomly freezes or locks up. Occasionally these locks are temporary, and then the computer resumes function as normal. Other times however, the computer locks up until a hard reset (when it does this, the sound also begins an endless loop of the same sound although eventually it progresses into a different sound but still very choppy and looping).

This is a seriously annoying problem, since it is so random that we have to constantly be saving work on the computer so that we don't lose it. The computer is used for a home business, and is only used for Quickbooks, internet and internet radio. The occasional card program or some such, but never anything too intense.

The computer is an older HP. It has an Athlon processor and 2056mb of RAM. I purchased a new hard drive for and installed a fresh copy of Windows 7 Home Premium 32bit. I checked the hard drive with diagnostics and everything checks out. I ran Memtest for 24 hours and got 0 errors with the memory. I've also stressed the CPU with Prime 95 and have not experienced the issue. It seems to happen randomly and with 0 warning whatsoever. I am completely stumped as to what the problem could be. I'm hoping some of you have some advice for me.