Can't boot

I'm new to this forum and hope that someone can help. I'm fairly computer savvy and do most maintenance and repair on our small office computers. Both are HP P7-1202 with 6GB memory and a Seagate 7200.12 1TB hard drive. My problem is that one of the systems won't boot. It has been acting funny (stopping, sometimes screen flashing blank) for a few days. I thought the hard drive was failing,...