Not necessarily!
Does
Ctrl+Alt+F2 switch you to a terminal screen? (Press
Ctrl+Alt+F7 if you wish to return to GUI.)
If the installation "did not finish," then of course the state of your overall configuration is unknown.
But as things stand now, it seems quite possible that the problem is with X-windows. If your system got all the way to a graphic login screen, the kernel probably
isn't the problem.
From the terminal-screen, login as
root, then
cd /var/log. Do
ls to see what files are there. Try:
less messages ("Q" to exit) to see if there are any useful messages. Try the same
less command against other files that are in the same place.
The problem could be with
gdm specifically. You don't know yet...