1) Check if you're connected. Run a terminal and
ping -c 4 www.linuxquestions.org
If you get numbers, you're conected.
2) Then ping one of your mail servers.
3) If you can ping, it's Kmail settings problem. Look if the adresses you entered into the configuration are 100% correct.
4) If you still cannot connect, run another mail program (the one from Mozilla or Pan or...) and see if it works.