The system sounds really unstable. It does not sounds to me like you have a bad hard-drive (unless it would have some bad blocks and that would stop the installation because it couldn't write to those. Howwever, that wouldn't cause system lock-ups after installations. I'd say to check the memory and the processor. Most unstability come from those. Is the system's temp ok?
If that is fine, do you have access to another processor or another memory module you can try? Perhaps borrow one from a friend? Is there any new BIOS version for your motherboard?