To get the exact model of the broken laptop, you can enter the system serial number on the check coverage page (please do not post the serial number on this forum since it is considered personal information):
Check Your Service and Support Coverage - Apple Support
You can try connecting an external display.
However, you may need to try putting the laptop into Clamshell mode by connecting a wired USB keyboard & mouse, plus connecting the power adapter & external display to attempt to use the laptop with just the external display. This is not always easy to do....sometimes it can be impossible depending on the model & whether macOS is running an update "questionnaire". You may need to toggle screen mirroring by pressing Command + Brightness Down (not always possible on the Login screen).
Perhaps you can use Target Disk Mode.
Make sure you have frequent & regular backups of your new Mac since there are a lot more new ways to permanently lose access to the data on the internal SSD due to all the hardware, software, and security changes.