I just finished upgrading Fedora 22 to Fedora 23 Beta and upon rebooting, gdm no longer started. I tried to reinstall the VirtualBox Guest Additions; unfortunately it still didn’t fix.
To cut the story short, someone has given a working tip at this forum. The solution is to downgrade xorg-x11-server-Xorg package.
# dnf --showduplicates --allowerasing --releasever=22 downgrade xorg-x11-server-Xorg
# mount /dev/cdrom /mnt; cd /mnt
# ./VBoxLinuxAdditions.run
# reboot
After rebooting, I was able to login again.
Credit: http://forums.fedoraforum.org/showthread.php?t=306857