If you're not seeing messages related to power or your hard drive, the first thing I'd check would be RAM.
http://www.memtest.org/
I'm not sure from your post if you are implying that the problem may be related to power management, but if so - try booting without ACPI (there is an option to do so from the boot menu). IIRC, APM is disabled by default. Does the problem go away when you boot without ACPI?