no offence dude, but please read back through what you write before you press the post button, I spend more time trying to decipher what you are saying, then trying to help solve your problem.
There are not many reasons the xbox would completely shut down, a short circuit, or an over heated gpu
you say there is defiantly not a short circuit so:
thought #1
where are the original Xbox 360 fans? Did you take them out? The xbox will shut itself down if those fans are removed; I think this is just a thermal sensor on or near the gpu. You must force the air from your new fan into the shroud in order to properly cool the gpu. NOT GOOD
but this xbox works when the fan is not inside the xbox this don’t make any since.
Thought #2
could you be blasting the original fans with so much new air, that it is deflecting the air from the original fan, thus not properly cooling the gpu, and when it is outside, it is more restricted and allows the original fan to blow at the gpu properly? NOT GOOD
thought #3
are you blowing into the exhaust ports? If so you are blowing hot air onto the gpu and tripping the thermal sensor. NOT GOOD
this is odd, if it works fine without the fan drop the fan. and move on...GOOD