Hello Matthias,

Error 1603 is normally an indication that something is missing in the installer.  I'd redownload the 2015 installers to make sure you did not get a corrupt download, and then try again.  If this doesn't help, and the advice Walter has provided doesn't help either then you should log a support case and a support engineer will help to sort this out.

Go to the Knowledgebase;

http://kb.sdl.com

Then go to the tab called Solution Finder ( http://kb.sdl.com/?cid=23&tab=sf ) and now go here;

Download & Installation Problems
- I use SDL Trados Studio and/or SDL MultiTerm 2011, 2014 or 2015
-- I receive an error message during installation
--- I have disabled UAC during installation / I do not have Win Vista 7/8
---- None of the error messages match my issue / I tried the suggested resolution....

So if you have tried everything suggested, when you get to this point you'll be presented with a form to contact support. Complete all the fields in the form making sure your email address is entered correctly or nobody will be able to get back in touch with you.

Also use the Chrome browser to log the case if you have it; you'll get more success in completing the form.

I hope this helps.