I used Camera Raw 8 to cut out an area of a DNG-file and saved the cropped image as a DNG-file again. I want to convert the cropped DNG-file into different TIF-files with different color profiles and gamma values. When I use dcraw, it always renders the whole image not only the cut out area. Is it possible to render only the cut out area using dcraw?
No, dcraw as a command-line tool does not have that feature. It's really not meant to be a full - fledged utility in itself.
If you are doing this with a photographic result in mind, I recommend a higher-level program, like Rawtherapee or Darktable.
It sounds like you are really looking to do your own processing / analysis. In this case, you probably should look at modifying the source code or building a program that does what you want around dcraw (or libraw).