So pc start's then shuts itself down???
Possible short somewhere maybe??
Is that cooler one of those AIO jobbies? If so inspect with a fine tooth comb/torch for possible leaks, i would take it out of your pc for this.
Edit, just because it works i would still inspect that cooler, gpu's can just die or there maybe a reason, if it does leak i presume your psu is below your gfx card and that could go bang! Better safe than sorry.