Computer turns on by itself

Hi
My nephew has an Evesham Decimator computer, with an FX55 AMD processor, runs windows XP, has an infrared mouse and keyboard, he has had a problem with it as for no reason it turns itself on, once when his mother was dusting next to it, it turned on, one night when he was asleep in bed, it turned on and it has done the same at other times once again for no reason, Evesham say there is no problem that they can see, can anyone shed some light on this, I've told him to go to Major Geeks site and download various anti spyware, cleaners and anti-virus software in case its someone trying to hack in, is that possible that someone can hack in to a computer that is turned off and is connected to broadband? any ideas please.

 

Thankyou will pass on information to my nephew, unfortunately I am getting ready to go back to work today (work abroad) so will have to get back to you when I get home in a months time.

 

also sometimes you can set your bios to wake your computer when your keyboard and/or mouse is touched-