Random no signal and slow boot time

Did they use your power supply or their own? And if their own which one did they use?
What would happen if your PSU can't cope with the load? Here are a few possible issues:

bad 3D performance
crashing games
spontaneous reset or imminent shutdown of the PC
freezing during gameplay
PSU overload can cause it to break down.

The psu is one of the MOST important components in your machine. If you don't get a good brand name and adequate power across the board then you're going to have these kinds of problems.

The other thing I can think of is temperature inside the case. open the side and see if it last longer - as long as it's fairly cool inside your room of course. Try monitoring your temperatures of the gpu and cpu and chipset in general. Heat will cause freezing and shutdowns also. The slow boot times could be an after effect of windows not shutting down properly. That, and your components might take a while to cool off if it's a heat problem.

i am pretty sure my PSU is not broke because i have used it on my other pc with the same GPU

So what psu did they use to test the kit?
What about the other suggestions? Have you tried any of those?

i updated the driver yesterday and played 3 hours straight with my case open
today i closed the case and it had a shutdown.
so im geussing that my pc is overheating, and how do i fix that without watercooling.

they used a 500W PSU from be quiet also.

today i had a shutdown again but this time with the case open