Try the File Expert method (
How to Sideload Mobi books without Restarting).
I also suggest connecting via USB and confirming that the MOBI files you downloaded via the browser are in Books or Documents and that they can be read from there from your PC (i.e. actually are good MOBI ebooks). On Windows, you can use Desktop MobiPocket Reader and on Windows or a Mac you can use
Kindle Previewer to check the MOBIs.