I have a 2008 model T3062 E machine that turns itself on and off by it's self1 person needs an answerI do too

Please elaborate. When does this happen? Does it happen while you are working on the computer? Is there anything logged in the Event Viewer log? Disable automatic restart on system failure and see if you get a BSOD with useful information:http://search.yahoo.com/search;_ylt=A0oG7hOL5cZMkFQA4aKl87UF?p=automatic+restart+on+system+failure&fr=yfp-t-701&fr2=sfp&iscqry=John

I get this quite often at work and the most common cause is that a windows update has installed in the background and the system is basically re-booting itself, giving the appearance that the PC shuts itself down. It should prompt you with a message but sometimes this can flick up when you press return and you don't see the message from Windows asking to re-start.It may well be down to what John suggests above so is also worth sonsidering.