Computer just turned on by itself but nothing is happening - and it wont turn off?

Well, that's a really weird one. Usual problems with power is the system doesn't power up but yours is the opposite. But anyway, it is still under power problem. Try to replace your PSU (power supply) with another, but ofcourse with the same rating as the previous one. You don't have to buy a new one at this point. Try to borrow one from your pals first. If the problem didn't came up with the new PSU, then your PSU is bust. If not, then onto the next! This could be mechanical. Your tower's front panel power switch maybe busted.