Check your /etc/resolv.conf file and see if it has something like this:
search smoker local
nameserver 18.104.22.168 #kppp temp entry
nameserver 22.214.171.124 #kppp temp entry
That is the first thing Mozilla and such looks for when it tries to find the net. If it has none then you may need to get them from your ISP. Kppp should get them when it logs in but your ISP may be different. The numbers after nameserver will be different for you. The ones in mine may work but they will be very slow, since we are on opposite sides of the globe.
One other thought. If you have a saved session and Mozilla opens when KDE is coming up, it may not work. I do not know why but I have to open Mozilla manually and it works fine. If I let it do it as a saved session then I have to close Mozilla then reopen it. No clue why.
Konquerer will work fine though.
Hope one of those will work, if not, clueless.