The problem is a malware/adware called "WajamInternetEnhancerApp.exe".

I observed some interesting/strange behavior. To use an UMTS stick I changed the internet access mode from WAN only to 3G/4G only and everything worked well. Back at home a forgot to change it again...

Thank you joyce, now everything works fine. The crucial note was to switch the router to 3G mode, which is a bit confusing, since 3G is a mobile communication standard and I have a cable modem. But...

There is only one dhcp server to configure. The warning is shown in the following picture: https://dl.dropbox.com/u/20555698/status1.png.

According to the web interface of the router, the dhcp server of the device will not start, if the dynamic IP mode is chosen.

jimasek wrote Switch off WPS (disable) and configure Wireless Security without key (free wireless access). I did both, but after choosing Dynamic IP, the router doesn't answer under 192.168.0.254.