Mountain Lion no login field after booting
The problem is that OS X detects 2 monitors and thinks that the secondary monitor is the main one.

This can happen with a monitor connected to the Thunderbolt port or in your case, as you state in a comment above, using virtual monitor software Air Display.

Apparently, Air Display didn't detect that the built-in MacBook Air monitor was active, so it sent the video signal over WiFi to a peer Air Display device. 

As a consequence you only saw the bare splash screen.