I want to enter HPC via the remote desktop by clicking the 'MATE' option, but it continues to show that it failed.

Before you can use NICE/DCV on Elwetritsch (https://elwe.rhrk.uni-kl.de/elwetritsch/zugang_tuk.shtml), you will have to log in via SSH or RDP to have your account created inside the cluster. After you have logged in via RDP or SSH, please wait for an hour until you try to use NICE/DCV again.

The reason: NICE/DCV submits a job to the cluster, and your account is yet unknown to the batch system.