Now this is getting more strange. We popped a couple of disks into my BFs disk drive and they installed flawlessly on his computer. Then he took his disk drive and connected into my computer. But I still get the CRC-error every time, even after I replaced my DVD-drive with his.
He says there must be something wrong with my hard drive, instead of the disk drive. So my next step is doing defrag on my computer. Its not too long since I did it but let's see if it changes anything.
Next step would be me chanting and dancing some good-luck-bringing dance around the computer under bare moonlight, praying to the mighty Computer Gods while my man is cursing and trying to fix my computer for this silly game...
(that one was a bad joke)
Thanks a lot PJSim and ChronicR, everyone on this forum has been so helpful during the months I've been a member. This forum really is a source of a lot of great information and help. Thank you.
EDIT.
In case someone will encounter this problem later, here's a solution which seems to work so far (I have installed the base game and WA and patched them; I got CRC errors installing both and also patching them both!)
To avoid CRC errors, do not install by the autorun prompted when you pop in the disk, instaed check out the contents of the disk, find the setup.exe, right click it and click "run as a system administrator". I avoided all CRC errors this way and the game is running fine so far.