The server does not boot. How to find the problem?

Question

System administration

The server lived. I decided to update and reboot. The update failed. And after a reboot it stopped responding. Launched rescue mode. The disk is whole, the server is working. The problem seems to be with the software. The server itself is the most common Ubuntu 18.04 (or 16) mysql + nginx + php-fpm the rest is standard programs.

boot.log

[^[[0;32m OK ^[[0m] Started AppArmor initialization.
[^[[0;32m OK ^[[0m] Reached target System Initialization.
[^[[0;32m OK ^[[0m] Listening on UUID daemon activation socket.
[^[[0;32m OK ^[[0m] Started Discard unused blocks once a week.
[^[[0;32m OK ^[[0m] Listening on D-Bus System Message Bus Socket.
[^[[0;32m OK ^[[0m] Reached target Sockets.
[^[[0;32m OK ^[[0m] Reached target Basic System.
Starting OpenBSD Secure Shell server...
[^[[0;32m OK ^[[0m] Started BIND Domain Name Server.
[^[[0;32m OK ^[[0m] Reached target Host and Network Name Lookups.
Starting Login Service...
Starting LSB: Record successful boot for GRUB...
[^[[0;32m OK ^[[0m] Started Daily apt download activities.
[^[[0;32m OK ^[[0m] Started Daily apt upgrade and clean activities.
Starting OpenNTPd Network Time Protocol...
Starting Accounts Service...
Starting Permit User Sessions...
[^[[0;32m OK ^[[0m] Started Regular background program processing daemon.
[^[[0;32m OK ^[[0m] Started Daily Cleanup of Temporary Directories.
[^[[0;32m OK ^[[0m] Started Message of the Day.
[^[[0;32m OK ^[[0m] Reached target Timers.
Starting Dispatcher daemon for systemd-networkd...
[^[[0;32m OK ^[[0m] Started irqbalance daemon.
[^[[0;32m OK ^[[0m] Started Set the CPU Frequency Scaling governor.
[^[[0;32m OK ^[[0m] Started D-Bus System Message Bus.
[^[[0;32m OK ^[[0m] Started Login Service.
Starting System Logging Service...
[^[[0;32m OK ^[[0m] Started Permit User Sessions.
[^[[0;32m OK ^[[0m] Started OpenBSD Secure Shell server.
Starting Terminate Plymouth Boot Screen...
Starting Hold until boot process finishes up...
[^[[0;32m OK ^[[0m] Started AppArmor initialization.
[^[[0;32m OK ^[[0m] Reached target System Initialization.
[^[[0;32m OK ^[[0m] Listening on D-Bus System Message Bus Socket.
[^[[0;32m OK ^[[0m] Started Daily Cleanup of Temporary Directories.
[^[[0;32m OK ^[[0m] Started Message of the Day.
[^[[0;32m OK ^[[0m] Started Discard unused blocks once a week.
[^[[0;32m OK ^[[0m] Started Clean PHP session files every 30 mins.
[^[[0;32m OK ^[[0m] Listening on UUID daemon activation socket.
[^[[0;32m OK ^[[0m] Reached target Sockets.
[^[[0;32m OK ^[[0m] Reached target Basic System.
Starting Accounts Service...
Starting Fail2Ban Service...
Starting OpenBSD Secure Shell server...
[^[[0;32m OK ^[[0m] Started irqbalance daemon.
Starting Permit User Sessions...
Starting Dispatcher daemon for systemd-networkd...
Starting System Logging Service...
Starting LSB: Record successful boot for GRUB...
[^[[0;32m OK ^[[0m] Started Set the CPU Frequency Scaling governor.
[^[[0;32m OK ^[[0m] Started Regular background program processing daemon.
Starting OpenNTPd Network Time Protocol...
Starting The PHP 7.2 FastCGI Process Manager...
[^[[0;32m OK ^[[0m] Started D-Bus System Message Bus.
Starting Login Service...
[^[[0;32m OK ^[[0m] Started Daily apt download activities.
[^[[0;32m OK ^[[0m] Started Daily apt upgrade and clean activities.
[^[[0;32m OK ^[[0m] Reached target Timers.
[^[[0;32m OK ^[[0m] Started BIND Domain Name Server.
[^[[0;32m OK ^[[0m] Reached target Host and Network Name Lookups.
[^[[0;32m OK ^[[0m] Started System Logging Service.
[^[[0;32m OK ^[[0m] Started Fail2Ban Service.
[^[[0;32m OK ^[[0m] Started Permit User Sessions.
[^[[0;32m OK ^[[0m] Started Wait for Network to be Configured.
[^[[0;32m OK ^[[0m] Started Login Service.
[^[[0;32m OK ^[[0m] Reached target Network is Online.
Starting Munin Node...
Starting nginx - high performance web server...
Starting Terminate Plymouth Boot Screen...
Starting Hold until boot process finishes up...

What other logs to see? no KVM.

Answer 1

Lived a server without KVM. Ivanushka-admin updated a whole bunch of packages, including, apparently, the core-pure emerald - the mouse ran in, waved its tail, and the server dropped.
That's the end of the fairy tale, but the moral is: a server without remote access - sooner or later to a long journey.

Answer 2

Simple googling suggests that with a probability of 90% you have no disk space left (clean it up).
With a probability of 5%, the problem is related to the plymouth package (which is not needed and can be removed, I myself encountered glitches in this package).