I upgraded Ubuntu 12.10 to 13.04. And now after boot no login screen appears, instead the screen just shows a kind of static noise. However booting and logging in with the recovery mode works without any problem.
The PC is running with a Radeon Mobility 4570, Ubuntu displays VESA M92 as driver. I find it strange that I have no problems with the Live CD of Ubuntu 13.04, the issue only appeared after booting it from the HDD.
(In a related question somebody suggests to edit the unity-greeter.conf file, but it seems this file does not exist on my system.)