Hello,
here is what I found out: In my template I use Bootstrap (the version which is coming up with Joomla itself). And I use the Bootstrap CSS Bootstrap v3.1.1.
In Line 7 of bootstrap.min.css I found Class "modal" which was set on "display: none" by default.
Overwriting this class makes the Modal Link visible (and usable). The Media field doesn't look that nice like in the protostar template, but i think with overwriting i can make it nicer!!!
Hope my answe will help any other people :-)
Thank you Ocotopoos for your hint ;-)