New build computer - power problems

EDIT: Turned out a pin in one of the cabels was 'pulled out' by connecting it with another cable. So just 3 out of 4 pins were connected which was the reason it wouldn't boot. Everything is fine now.

Hi,

I've build a new computer for my mother yesterday and I've ran into a few errors now. This has been the first time I build it 100% on my own without the help of my father so this annoys me quite a lot. When I first finished the build it wouldn't power on and I had no idea why. I asked my dad to help and he couldn't figure it out either. As it was getting pretty late I went to bed and in the morning my dad looked at it for like 30 minutes and he got it working but he wasn't sure what he changed.

When I got back from college today the PC worked great and I installed windows 7, microsoft office, java, flash and updated all drivers so the PC was good to go for my mother.

So I unplugged everything and set it up downstairs but for some reason it wouldn't turn on. I was rather pissed off as it was working without any problems 5 minutes ago and the only thing I did was bringing it downstairs and plugging in some stuff.

I opened the case again and pressed a bit on every cable to make sure it was connected properly and turned it on using a different wall socket. And it worked. So I put it back under my mothers desk and plugged everything in again... but it wouldn't start.

Pressing everything again and making 100% sure everything is connected I set it up again without any cables except for the PSU. Turned it on and it started without any problems. I shut it down and added the other cables and it wouldn't boot up anymore...

After playing around a bit I got it working with a monitor now but for some reason the BIOS got corrupted and I had to do a system restore. Now it is running but I lost java/flash/office because of the system restore. So I planned to wait until my dad got home to look into the problems together so I shut it down. But for some reason it does not shut down but it shuts down then reboots after 2 seconds.

I'm not sure what is wrong but I'm thinking that the PSU or motherboard is partly broken or something? Any idea's? Very frustrating.

EDIT:
Specs
Intel Core™ i3-3220 CPU
Be quiet Pure Power CML8 430W PSU
Coolermaster Silencio 450 case
Gigabyte GA-Z77-D3H (rev. 1.0) mobo
Corsair 4 GB DDR3-1600 ram
Those are all new, combined with a 750 GB HDD & DVD drive