Hello @Malte M. Thank you for your message. I am available even now for a call. I am working from home now due to the pandemics, and to have internet connection is really critical and urgent for me.

I have used the diagnosis on telekom.de and it checked the connection and replied the following messages:
- the router was offline
- Since I double-checked the DSL cable and it was connected firmly and in the correct slots/ports, the diagnosis tool asked me to connect to a different internet source (which I already was connected to as I do not have the internet at all via a router) and started the restarting of the line. After few minutes of waiting the connection error appeared. I tried to continue this diagnostic a few times - but every time it crashed and no changes were made. Still do not have internet.
When I remove the DSL cable from the router - no changes appear - still two lights on (Status and WLAN) - it seems that the router does not see the cable at all or there are no any network connected to this cable.
I had this internet for a month and half and it was generally ok. Just few times week. the router was loosing the connection and then in few minutes of appeared again, which is inconvenient as well, but not as full lack of service.

As well, hope it will help you to see some diagnosis details eventually- I have reported this fault via the telekom.de tool and it was registered with No. 266307044 (11.01.2021, 18:29). Thank you.