i had forgotten the root password. In the GRUB menu, I pressed e, and added “rw init=/bin/bash” at the end of the first linux line.
I did an F10, and then changed the root, and user passwords.
I rebooted, but the GUI did not recognize the user and password combinations.

I rebooted, and entered the F1 console. F1 recognized the passwords. As user I entered startx, and it got me to the Welcome screen. However, now, when in an xterm, the passwords are not recognized. I rebooted and repeated the process. The passwords were recognized in F1. However, this time startx did not work.

I later tried startx and it worked.

I can get in using startx in F1, after a couple of attempts, but not through the GUI.

I reinstalled mdm while in F1; but that didn't help.

I suspect the keyboard layout changed between root and GUI sessions. Or do you use English (EN-en) in both? Then this guess is invalid...

X and the console use different keymap files. The X keymap is usually set by a file in /etc/X11/xorg.conf.d. That could cause problems if you are using a language other than American English.