Could be you have blown one of the chips on the MB - as such only when it is powered does it start behaving eratically i.e. shorting one of the imports to ground or similar...
when not powered the fault may not be servere enough to show up as a short.
Also when you say appears to be blown when powered - how have you measured that?
i.e. - are you measuring voltage on both sides and seeing a difference? or are you trying to measure resistance across the fuse when it is powered?
