I am having the exact same issue, it would seem, with my 2012 MacBook Air.
It started following updating to 10.8.5. I first noticed it when I tried to get on WiFi at a FedEx Office (AT&T WiFi). The login in screen popped up but never loaded.
I eventually gave up and tethered to my phone.
Later on, I tried to connect at a Starbucks (also AT&T WiFi) and no login screen was launched. Sometimes I could get an IP address, other times it was a self-assigned IP.
I could also not connect at the adjacent Einstein Bros. Bagels. Again, no login/authentication screen would launch on the MacBook Air.
This workaround, while a pain, has worked 100% of the time to address this issue.
- Authenticate to the commerical WiFi network from my phone
- Turn off my phone's WiFi
- Spoof my phone's MAC address onto my MacBook Air
- Successfully access the WiFi network
Unfortunately, I presently have no way of rolling back to 10.8.4, so it looks like I'll be doing this workaround until I either come up with a permanent fix or until 10.8.6 comes out and hopefully addresses this issue.
I have no problem connecting to either open WiFi networks or networks with WEP/WPA/WPA2 security. Only networks that launch login/authentication screens present this issue.