I stumbled across this thread while trying to debug my first Debian install (Buster 10.3 with Gnome) on an older Lenovo laptop. I had no problems with the install until a I booted for the first time and got to the GNOME Display Manager message at which point nothing further happened. Switching to another console and then back (ctrl-alt-f2 then ctrl-alt-f1) got the window manager to display, but on a reboot the display manager would not show the login screen again,
So as suggested, I took a look at the contents of /var/log/Xorg.0.log and then verified what VGA controller I had using
This told me I had an AMD GPU but that the Xorg.0.log file indicated that it couldn't find the driver for the particular graphics controller I had. Searching Debian's site, I found that firmware-amd-graphics had support for my card but was not currently installed on my system. So I installed that via
Code:
sudo apt install firmware-amd-graphicis
I then rebooted and all is working properly now.
While I can't be 100% certain that what I was experiencing was the same problem as seen by the OP, I suspect they are likely the same. So hopefully this post helps someone in the future with a similar issue.