Kernel panics are usually hardware related in my experience, I'd unplug all unnecessary usb and pci cards, then iso-image boot to run memtest86 on it. If you can see the logs of the panic or leading up to it, see what component or driver is complaining, but if nothing else after everything is removed, I'd suspect memory, maybe even power supply. Rarely see a cpu or mobo die unless it's got blown capacitors.
If nothing else, boot clonezilla iso (I think it should have memtest86 too), or any other linux boot cd and copy/clone the disk data that way to a target disk (ie usb), mounting your drive volumes as needed. About as painless as it's going to get short of connecting the disk in another working linux system via usb carrier or direct.
-mb