Judging by the label in the Wi-Fi menu at the right of the top bar, my MacBook is connected just fine to the Siemens Gigaset SE567, which I'd like to use as a wireless router.
Judging by the lights on both the router and the cable modem (Motorola SB5101 Surfboard), that connection is also good.
But I am unable to ping anything outside. I'm also unable to ping the modem (if I connect to the cable modem directly by ethernet, pointing a browser to http://192.168.100.1 is all that's needed).
What's a good way to debug this problem? I "can't open the application TELUS High Speed Install Wizard" (the one that came with the modem) "because PowerPC applications are no longer supported" on Lion.
According to http://www.networkoverload.com/forum/networking/turn_your_gigaset_se567_modem_wireless_switch_bridge_mode one can indeed configure the SE567 as a wireless router, though I don't understand whether more than one computer could then connect to the network.
After resetting the router, I was able to connect to its configuration at http://192.168.1.254/ (strangely, resetting did not wipe out the previous SSID name).
As the page above suggested, one needs to switch to the "bridge mode", but after doing so, I can no longer connect to http://192.168.1.254/
Since this is looking more and more like something that can be resolved by accessing the web servers on the two devices rather than by tinkering through System Preferences \ Network, it is not quite the right thing to ask on this forum. I will delete the question if it turns out the mac is incidental to the setup.