Judging by how it will shut down after rebooting, before the operating system is even loaded, I think overheating is a likely possibility. Go into the BIOS, and see if it has an auto shutoff temperature. Try a program like Speedfan
to keep track of fan speeds and temperatures. I would also check to see if there are any BIOS updates available, as it could be a problem with the motherboard reading the battery charge status incorrectly.