I'd suggest not using Kinternet for wireless connections.
What Suse version do you have? 10.0?
I'd suggest installing netapplet for 10.0 and knemo, both of which are available in Software Management.
As for your problem on connecting to the internet, you might want to use the command shell. Open a Root shell and type "ifconfig". That shows you what network devices are on and what their IP address is and whats happening w/ your packets.
"iwconfig" shows you what wireless network you're connected too.
Chances are if you can get to your router, but not the internet, then its a DNS problem. I'd then suggest going to Control Center, Yast Modules, Network, Network Devices. Then you should see your wireless card there and I'd take a look at your hostname and DNS information there. My dad's machine had a wierd glitch where Suse grabbed the wrong info for the DNS server IP address and I had to manually configure it.
Hope this helps