@T1125P I haven't read Jerry's links so sorry if what I'm gonna say is in there.
My previous DELL (before my 6530) had the same issue.
If the AC adapter was not present everything was OK but if it was plugged in, Shutdowns turned into Reboots.
In my case, tried with another adapter, same thing so it was caused by the laptop's internal power module.
Hope this is not the case for you!