Thank you
Northernsoul55 - it's not necessary anymore - Problem solved.
Here's the solution:
Solving this was a bit tricky, because TWO things were the cause. There was also the well known problem involved that the 3TB dive only showed 746 GB available.
I have a quite dated Gigabyte GA-P35-DS4 Motherboard. The BIOS needed to be updated to the latest Version (14)
The next and most important step was to update the Intel RST Drivers.
On some other Board I found a solution where someone was updating to Version 10.8.0.1003 and it worked for him.
So I went to the intel site looking for the newest Drivers.... but the refused to install. I guess I downloaded three different packages and I also tried to install manually. None of them installed - I got either a "platform not supported" or a "your driver is up to date" error.
In the end I did a search for the exact version Number (thank god the number was included in the post ; ) and installed the package.
After rebooting everything was fine! The drive showed up normally in Disk manager and everything works perfect.
In case anyone has a similar problem - here's where I got the Intel RST package from. (I actually had that the intel chipsed driver installed before.. but my version was outdated)
Intel Rapid Storage Technology Driver (AHCI) 10.8.0.1003 Driver for Windows XP / Windows Vista / Windows 7 Free Download
PS: the site is full of those "download" links we all love so much... make sure you pick the right one.
I also copied the link location of the correct download button... but I do not know if it will work if the other crap was not clicked before.... so just in case here it is:
Download starting...
Good Luck