Does it sound possible that your disc, or that partition of disc, is « full » ?
df -h
will show storage capacity of your partitions.
ncdu
is a simple tool to check your disk usage ( use ←↑↓→ keys to browse ) and eventually delete files and folders ( hit d key as delete and ? for help ).
To install it
sudo apt install ncdu
Often culprits for disk usage are old linux kernels.
sudo apt autoremove --purge
may free some space by deleting unused packages, including older unused kernels from automatic updates ( not the manually installed ones ).
And also
sudo apt autoclean
by cleaning local indexes of no longer useful downloaded packages ( my pity translation sorry )
Anyway I am not sure a full disk explains why you can’t acces your desktop.