The other day when attempting to start up my system, I got greeted by the following screen after having have logged in:

A password is required to access the volgroup volume:
Enter passphrase for /dev/sda3:
/dev/mapper/volgroupo-lu_root: recovering journal /dev/mapper/volgroup-lu_root primary superblock
features different from backup, check forced.
/dev/mapper/volgroup-lu_root: Feature orphan_present is set but orphan file is clean.
CLEARED.
/dev/mapper/volgroup0-lu_root: 248789/1966080 files (0.2% non-contiguous), 2301463/7864320 blocks
[FAILED] Failed to start Remount Root and Kernel File Systems.
[FAILED] Failed to start Virtual Console Setup.
[FAILED] Failed to start Remount Root and Kernel File Systems.
[TIME] Timed out waiting for device /dev/disk/by-label/ESPO.
[DEPEND] Dependency failed for /boot/efi.
[DEPEND] Dependency failed for Local File Systems.
[TIME] Timed out waiting for device /deu/disk/by-label/maino.
[DEPEND] Dependency failed for home.
[DEPEND] Dependency failed for Grow File System on /home.
You are in emergency mode. After logging in, type: "journalctl -xb" to view system logs, "systemctl reboot" to reboot, or "exit" to continue bootup.
A Give root password for maintenance
(or press control-D to continue):
'bc' not found.
Aborting: 1 commands were missing. Please install needed packages.

Despite countless restarts, shutdowns (with and without power cord unplugged for appr. a minute) and endless hours scouring the web and archlinux forums, etc., I have yet to find a solution or anyone with the same problem for that matter. I tried: sudo pacman -Syu, checked for internet connection, where I found out that, in spite of following many different instructions from various sources, my ethernet PCIe slot is regocnised, the ethernet cable is working, I cannot however find my local network, neither through WiFi or Ethernet (Lan).
I'm using a late 2013 mac mini, broadcom PCIe for internet is built into that. I do not know what the problem is: Is it the fact I do not have WiFi/Lan or is there something else that is broken. I want to know and learn everything there is to linux and computing and solve presented problems, I am however a noob when it comes to this. This is why I am asking You for help!

Not sure this is exactly the same, but maybe it can lead somewhere:
try this

Cy10001,

Are you able to boot from the installation media and then access Terminal?

If so, let us know the output of these 2 separate commands.

Click on the #above to wrap the copied and pasted output in Code tags.

Could you have enabled lux encryption?