Hi there. This sounds like an issue that gave me a lot of grief - took me months to solve - and it's a pity you've only had one other reply so far. I hope you're still there.
OK. I'm assuming that the router is acting as a DHCP server and that your other PCs are running either Windows or MacOS. If so, this may be an IPv6 issue, and there are three solutions, all of which worked for me.
1 Disable IPv6. You have to edit a .config file somewhere. Can't remember the details and different distros put the file in different places. If you want to try this, search this forum, do a bit of googling or hope someone else answers this thread.
2 Go into Yast/Network card. Disable DHCP and enter a static IP address and DNS address(es) manually. DON'T put in your DNS addresses with DHCP still configured. If you do, it will all work for the current session, and then when you reboot, you'll find the DNS address set back to the IP address of your router.
3 My favoured solution. I upgraded the firmware for my router, and then everything JUST WORKED!
I believe that the old firmware was being confused by IPv6 addressing. Apparently, firefox uses IPv6 modified IP addresses (or something like that) whereas Konqueror still uses IPv4. But perhaps someone may correct me.
I wish you luck. This may not be the answer, but please post back with whatever you discover.