My problem has been solved!
I've downloaded and installed all the files on my laptop (which went without any problems whatsoever) and then copied the folder to an external HD and copied it over my folder on the PC.
And it actually worked!
So, for everyone out there that has been unable to install SWTOR:
1. install SWTOR on another PC (or better yet: Find a friend who plays SWTOR as well and has already installed it)
2. Take a copy of the entire "Star Wars-The Old Republic" folder
3. Make sure the folder on your PC has the same name (For some reason it was called "Star Wars - The Old Republic" on my PC and without the spaces before and after the "-" on my laptop. (Did not change any locations so I dunno why this is...)
4. Copy the working folder over your broken folder. Press Yes to all.
It's really that simple...
And once again thank you BW for your efforts in helping me, good luck with all the others!
And now I'm off geek out and make my character! ^^