I cleaned the 32-bit version so the 64-bit version ain't installed on top of the other. I did remove everything and did a clean install without any success of installing the 64-bit version.

There are 32-bit versions of windows 7 - you are sure you have 64-bit OS?
A lot of installer is probably 32-bit, so it might not notice unless checking.

I'm running Windows 7 Ultimate 64-bit

You say you're running Win7 Service pack 1,  but your OS Version: 6.1.7600.2.0.0.256.1 as reported in the error log is for Win7 without SP-1.
 
Win7 SP-1 would be 6.1.7601.....  as here
 
 
You said you tried re-installing Windows,  make sure you have ALL the updates and it is SP-1.  (and 64bit)

My misstake making it a bit confusing there. The error log was from when I first tryed to install it. I updated to SP-1 just after and forgot to make a new copy of the error message there. It's all the same "same error message" now except that I'm running the SP-1. Still no luck in installing.

Just for kicks I would try installing to a different folder.   Also, if you're installing from CCC try downloading directly from your CW account and running the installer manually, and vice versa.
 

Thx, but I've already tried those things too without success. I'm really left clueless on how to proceed. Also tried installing on another hard drive...but still no luck.

The most common cause for this crash (recently) is incomplete windows updates (SVCR120).  Are you sure that all of the Windows updates have successfully been applied to your computer - including the reboots after the installs?
 
The most recent was running with an account that did not have Administrator permissions, even though run as admin was selected.  Did you have to enter the administrator password when installing?
 
Glen
 

I have installed all updates that been announced except for the language packages. I didn't have to enter the administrator password. Could this be it? My account is administrator with full rights. "I've triple-checked". I've tried the installation with CCC and manually, both by standard clich installation and by right-clicking and "open as administrator" but I did not once, except for login in to Windows, have to enter my administrator password during the installation process. Is there an update I may have to find manually? Because there's none to click on in windows update on the list.

ThIs
I've tried the installation with CCC and manually, both by standard clich installation and by right-clicking and "open as administrator" but I did not once, except for login in to Windows, have to enter my administrator password during the installation process. 

The normal response when starting app as admin is to get a dialog asking you to manually confirm this operation - elevating your authorization for that process. Just a Yes/no dialog.
 
No password required if you are logged into an account that belong to Administrators group.
If your computer only has one user account, seen at bootup, that is normally the case.
 
If creating users you must remember to add it to Administrators group.
 
If you don't get the dialog asking you yes/no - you might have UAC(User account control) turned off.
Not sure how that responds to different operations that need admin rights, though.
 
Running offline installers(any application) - I would always start with rightclick and run as admin to be sure.