I followed all of the steps to connect wirelessly to Raspbian for Robots. I am able to view and interact with the desktop when my ethernet is connected. I also have the wireless setup, and I am able to ping outside websites from the Raspberry Pi, and I am able to ping the Raspberry Pi from my PC laptop. But as soon as I disconnect the ethernet, I cannot open the desktop from the browser (but I can still ping the device from the PC).
I am assuming you’re using http://dex.local as the address in the browser?
Is Bonjour installed?
When the Ethernet is connected, and you can reach the Pi, can you find out its wifi address?
Open a terminal and type in ifconfig
you should have a section that starts with wlan0 and somewhere in that text there’s supposed to be an IP address. If there’s one, try using that instead of dex.local