Inability to connect to the internet should not cause the system to fail quite that drastically. I think you may have other problems, and their messages might have already scrolled off the screen. You could use Shift + PgUp/PgDown keys to scroll the messages backwards some amount; that might allow you to see the earliest abnormal messages.
At the top of your screenshot, there is a message:
You are in rescue mode. After logging in, type "journalctl -xb" to view
system logs, "systemctl reboot" to reboot, "systemctl default" or ^D to
boot into default mode.
Normally, there should be a prompt to enter a root password after this text.
But in your case, there is another message:
Cannot open access to console, the root account is locked.
See sulogin(8) man page for details.
Press Enter to continue.
This means the system was going to allow you rescue mode access, but there does not seem to be a valid root password available. You'll need to fix that first.
Reboot the system, interrupt GRUB when it displays the menu and press E to edit the boot options. Move to the kernel line and add init=/bin/bash to the end of it. Then press the appropriate key (indicated on the screen) to boot the system with the temporarily-modified options.
This should bring the system up to a point where only the root filesystem is mounted, and even that is in read-only mode, but you get a # root prompt straight away.
First, get the root filesystem into writeable state:
mount -o remount,rw /
Then, use the passwd command to set a new password for root. It will prompt you to enter the new password twice. If you plan to use characters that are not numbers or US-ASCII letters, use the command prompt to test the keyboard mapping before setting the password: it's possible that the keyboard mapping of your choice is not in effect and you're falling back to US English default layout in this mode.
Once you've successfully set a root password, it is time to restart the system again.
But because of the special way used to start the system, some special steps are needed.
mount -o remount,ro /
sync
reboot -f
On next boot, the system will probably again drop into rescue mode, but now there should be a prompt to enter a root password. Enter the root password you previously set, and you should get the root prompt. Finally you can follow the suggestion to use the journalctl -xb command to view the system log.
The logs will normally contain a lot of informational (non-error) messages. You should find the earliest error message; that is probably the root cause of the boot process going off the rails.
An alternative method for gaining access to a system that has severe problems is to boot from an installation media (e.g. your installation USB stick) using the rescue boot parameter. The installer will present the standard language/keyboard layout questions, and then switch into a special rescue mode that attempts to detect an existing Debian installation, mount its disks and provide you with a command prompt + a set of tools to fix things.
Oh, and to fix your missing Realtek firmware: use another computer to grab the firmware-realtek .deb package, save it on some removable media, move it to your computer and use e.g. dpkg -i firmware-realtek*.deb to install it.
