EDIT: I just tried flashing MIUI and CM9 via Kitchen Sink ROM and both did the same thing. Boots to lock screen then vibrates and shuts down.
EDIT 2: If it helps, this isn't my first time flashing a ROM, I've flash all of these multiple times, so I don't really know what the issue is.
EDIT 3: I just did 3 different restores including one to the original ROM, it did the exact same thing. I also tried 2 different batteries, both of which are fully charged.