Wheres the screw and standoff that used to be next to the CPU fan header?
This is true ^^ a Mobo should always be supported properly...
If you have a short your motherboard will shut down immediately or you will blow the PSU.
I dont think it is a short or it would do as sed above, or the washers, and yes corsair have pre-loaded thermal compound. However if you have removed the cooler you need to re-apply the compound as OhSnapWord told me tiny air bubbles can be trapped between the CPU and the cooler, resulting in poor cooling performance.
But to be honest i think you should test the set out on another computer, i think it may be faulty, the shutdowns are from CPU getting to Hot, not nothing else (i presume). Either this or you CPU_FAN port isn't working properly but you sed you old fans worked fine?
Test the corsair on another computer or enter bios and turn the multiplier down on you CPU, so the CPU doesn't work enough to get that hot and run some fan tests, and see if the fans slow/get faster.
My theory you have a faulty pump in the H60 and need to return it, but try everything before hand and be confident its broken before returning, many component stores test products sent back to them, to ensure there not being scammed.