I'm not sure if you are still trying to install or if you were able to install

using text mode or VNC.  Are you using Xorg or Wayland? Can you

connect to the system using ssh and view dmesg after the screen goes

blank? 

Usually there will be some error messages that you can use in web searches.

These days most problems are being discussed and bug reports filed by the time

I find the details in a log/journal.  Search for recent reports of issues with your

graphics hardware may find useful information.   The problem may not be directly

tied to the graphics hardware (e.g., power management glitches leading to

overheating on an older system with dust in the cooling fins) so you have to

scrutinize warning messages to determine if they are related to your graphics

issue.