connyosis

Ok, I really hope you guys can help me out, because this is way beyond me.
Today I assembled a computer for my girlfriend, something I've done lots of times before. So, all is well, I start the computer, enter windows and installs everything for her. When I'm finished, I close the case and stand it up. After a few minutes, the computer shuts down, just dies.
I'm wondering WTF and opens it up again, all looks to be alright. I turn it on, only to have it die on me almost right away.
After some time swearing and messing around, I figure out that the computer works just fine, as long as it's lying on it's side! When I stand it up, it's just a matter of time before it dies without warning.
Now, I suppose I could let my girlfriend use the computer lying on it's side, but somehow I doubt she'd like that.
Anyone has any idea what could be causing this? I have no ideas left...

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