I rebooted my computer and got sent to an initramfs prompt. There was an unexpected inconsistency error that required me to manually run the fsck command. So I did that, but now when my computer starts up the desktop is just a black screen with my icons on the desktop. Startmenu and panel can't be seen.

I tried recovery mode but I got the same result. I used the ctrl+alt+F3 shortcut to get to terminal and updated everything but still to no avail.

I don't know whats wrong and I have to use the library computer to get help.

Too little (almost no) info to work on, so ...

fsck fixes the filesystem, not necessarily any files within. Depending on filesystem type (hint: you didn't tell us) various parameters may take actions you don't really want to happen automatically.
So as a minimum we need the fsck command you issued with parameters, any messages it generated you can remember - and whether there were lots of them or just a few. And the distro, and the desktop. "lsblk -f" too ...

As a first step it might be that you can simply (???) re-install a destktop meta-package - varies by distro, but a quick search online should get you plenty of hits for the popular distros.
If it get too messy I tend to just reinstall ensuring /home isn't over-written. But that might depend on whether you use encryption, LVM, RAID ...

Hmm. Well I can tell you I'm working with Linux Mint. I can't remember if there were any notable messages after performing the fsck command. I did: [(initramf) fsch /dev/sda5 -y] as the command. Not much else that I can tell you.

I am prepared to just reinstall my distro but how do I do that without erasing Home?