This is not the ultimate solution but it may help to find out the problem..
On the pc that is playing up Do a properties on "my computer" then select the "Advanced" tab and then "start up and recovery" settings button then take the tick out of "automatically restart"
then apply/ok and you may have to reboot..
Then when the problem occours you will get error codes/info to work from and you will know its a software problem..
If the pc still reboots itself then it must be a hardware problem, I know you said that you checked ram and cpu but there still could be a problem somewhere with these or the mobo..
Hope this helps..