Fans Start Computer Dies

Having troubles with my computer, i press the power button and the fans kick in, 2 seconds later they switch off and the computer dies. Everytime i press the power button this happens.
Luckily (well i say luckily) i was able to save all of my documents and uni work by connecting my hardrive to my girlfriends laptop and transfer it all onto a portable hard-drive. Now tho it seems my girlfriends laptop is doing the same, when it is unplugged from the mains and the power button is pushed nothing happens, but when plugged into the mains the fans kick in for 2 seconds then the whole thing dies. Surely these two problems must be connected as from when i connected my hard drive to her comp, both systems had upto date virus checkers, any one have any ideas? also now she cannot access any of her documents and mine are all on my portable hardrive. If i plug either of these into another computer to try and access them will the problem happen again? If anyone could shed any light this would be much appreciated
Thanks