Sounds like the motherboard is shorting out somewhere.
- did you put the standoffs in the new case? (the little brass things that came with the case, on which the motherboard should sit)
- Did you by accident put a standoff which does not have a corresponding hole in the motherboard, thus touching the motherboard at the bottom
- Is there anthing metal that touches the motherboard, as far you can see? (edge of case, a bare piece of a wire, etc)
- Are all cables securely and properly connected?
If nothing of this gives a solution, then take everthing out of the case, put the motherboard on a flat antistatic surface and try to boot that way with only CPU/RAM/Video.