Can somebody help a beginner out?

I extracted my company logo in vector format from a PDF file and want to export it to a transparent .png image. This works except for the white areas enclosed by other colors. Basically the letters O D and A have white areas inside and I want them to be transparent too. I tried to select the white area and set the fill to none, but then the color of the object below shows up.

Can somebody tell me how I can manage to get those areas transparent too? Can I somehow select and cut out the white areas from the objects around it?
TIA.

Maybe:

Path → (Ctrl+K) Combine paths: Combine selected paths into a compound path. This will work for any set of paths regardless of how the paths are arranged in Groups.

http://tavmjong.free.fr/INKSCAPE/MANUAL ... iting.html

Thanks, will look into it at home.

Also make sure the path fill rule is even-odd.
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Attributes-Fill-Stroke.html#Attributes-Fill-Rule