turn on wireless and from kindle linux command line try to ping some hosts, for example:
ping -c 5 www.google.com
then if internet connection is working, you should see smt like this:
(18.104.22.168) 56(84) bytes of data.
64 bytes from fx-in-f103.1e100.net (22.214.171.124): icmp_seq=0 ttl=55 time=31.3 ms
64 bytes from fx-in-f103.1e100.net (126.96.36.199): icmp_seq=1 ttl=55 time=32.3 ms
if you see nothing, try to ping google's or other IP:
ping -c 5 188.8.131.52