Some websites don't respond to a ping, so pinging an external address isn't always a good test.
I would recommend doing a "traceroute" ("traceroute www.google.com
") to see on which hop it is failing.
Posting the results could help others help you.
There are many possibilities.
Do you have a correct default gateway configured for that machine?
It is unlikely, but entirely possible, that you have a firewall in-between you and the internet and it is configured to block the address of your Fedora server from reaching the Internet.