Ok, here's just a few more questions:
1. What version of DNN are you using?
2. How is this site hosted?
3. What module are you using to create your content? (Some modules use their own syndication methods)
4. Are you setting this module with the 'syndicate' option checked.
Now, the other thing to understand is that the News module is not responsible for the syndication of any content - period. There are internal methods for creating syndicated content with most DNN modules, and third party modules, but their issues are not really in the area covered in this section of the forums. You would be better served adding a thread in the module forum you are using.
You should not have to go to the 'FeedBurner' site to expose these feeds to the public. I've working on the earlier versions of internal DNN syndication, so I may be able to help with your issue after you answer the above questions. At this point I really can't say what is the trouble.
Cheers