Did your case come with any standoffs when you got it, or did the motherboard? I think they're all pretty standard anyway, so you should be able to pick up some from eBay.
Sounds like the board shorting on the case is your problem, do you have any standoffs installed at all? If you have too little installed, you may get issues, if you have too many and the standoffs are making contact with the board where they shouldn't be, you'll also get issues.