Well, received my DX58SO2 yesterday and I decided to try to just change the motherboard. 
And IT WORKED! 
 
Didnt even get a bluescreen! 
 
Just "plug&play" actually. Strange, as I was quite sure I had to install just about everything (both my OS drive and my programs drive) 
Well, happy days now :) 
 
And, just for the record. The strange cold boot failure is gone. So it actually was the Gigabyte mobo. 

With a different motherboard, it wll require installing device drivers.  Windows will automatically install some, but some will be generic basic function drivers and not the full driver.  For example, Windows will install the basic function "HD Audio Codec" for the PC sound driver.  For full functionality the Motherboard vendor (in this case) sound driver should be installed.
 
Since this is an Intel motherboard, go to the Intel site and let it scan the PC.  It will display what drivers are available or needed.  www.intel.com

Yep, I've installed the USB3 driver and SATA driver. 
 
I've disabled most other unwanted stuff in the BIOS (internal soundcard, LAN etc) so the HD driver wont be installed :)
 
FW driver did either install itself, or it is the same (I had to go into properties and change for legacy driver though)
 
And I tried to install the "intel-chipset-driver-package" from the intel site (from the DX58SO2 download section) but the installer told me I have a more recent one. 
 

If you are not using the devices then you are OK, at least now.  In the future if you decide to use them then you will have to get the proper drivers.  May be a good idea to enable all the devices, go to Intel and get the proper drivers and install them.  Then go back and disable them, then you will be set if you ever need to use one of the disabled devices. 
 
Windows must have installed the chipset driver.

I'm not sure, won't every Mobo that have intel chipset share the same driver package? 
Thats my impression 

Not always.  If you have, for example a G33 chipset and then change to H77 it would require a different chipset driver.  One of the main things a chipset driver does is define (identify) all the devices on a motherboard.  With different motherboards/chipsets the devices will vary.
 
I used to have an Intel DP35DP motherboard.  The intel list for the chipset that supports this board shows a lot of motherboards, but your specific model is not included.  A different version chipset is needed.
 
From the Intel site:

The Intel® Chipset Device Software installs the Windows* INF files. The INF files inform the operating system how to properly configure the chipset for specific functionality, such as USB and core PCI.
 
 

Check the boot order for the dives and the controllers in BIOS.  Sometimes, it defaults back to IDE when you're trying to boot from SATA.  Good luck.