In case the reboot in GRUB is due to faulty RAM causing a glitch, you could see if there's an option to disable "quick boot" or "fast memory self-test" or something similar in the BIOS settings. That would check the RAM more completely at start-up and possibly detect a failure that's missed during the default fast RAM test. Running Memtest86 would be better again, but that would need to be booted from a floppy or CD.
If there's more than one RAM stick installed, try booting with just one, then if it's the same try again with just the other stick.