This is a laptop with a broken internal display (”LVDS1” in xrandr output), and therefore connected to a working external LCD (”VGA1”).
After upgrading from Precise to Trusty, boot ends with a black screen (on the external display). The greeter sound effect is played. Typing my password (I’m the sole user) does log me in, and brings up the desktop on the display.
So the login functionality is there, just the visuals are missing. And they do flash by (corrupted) when the desktop is loading; if I set automatic login for myself, I get a desktop with the login screen as the background image (I’ll attach a screenshot).
There are existing, similar reports but all with subtle differences from this (such as Bug #1252748, where the user only gets black screen half the time) or too vague for me to claim to be the same issue with certainty (such as Bug #1242213). A lightdm restart (such as in Bug #969489) doesn’t fix this (i.e. black screen still after lightdm restart).
I’m not sure whether this is a lightdm issue or a unity-greeter one, so my reporting this against the latter is just a guess.