I had a similar problem with an old PC whereby the XP install would either BSOD, or it would say "cannot copy files". The latter lead me to believe the disc was bad, and when I eventually got it installed thought my problems were over. The PC started rebooting randomly and would turn on on it's own, I thought it was the PSU. took out one of my RAM sticks, now the PC runs perfectly and installs fine. So I would definately try either taking one stick at a time out if you are running in dual channel, or try some different RAM, possibly from another system.
Matt