Good. That makes it sound as if the Kindle wireless/WiFi ability has failed.
There are some things you can do:
1. if it's a matter of minor corruption of the Kindle's operating software, doing a reset back to factory conditions will erase everything stored on the Kindle - notes, bookmarks, books donwloaded onto it - but may restore WiFi connection. Back up notes and bookmarks, of course, first... if possible.
2. if it's a matter of the Kindle being 'broken', it can be sent to Amazon for repair - at cost to you, since it is out of warranty.
3. if it might just be something else... a good test first is to take it to another WiFi source, briefly, and see if it connects there, even briefly, after authenticating. If it does, then (1) and (2) are not the problem.