I tried "Change IP Addresses", and also used the DNS IPv4 from your screenshot and nothing changes on my end.

The Customer Service recommended a reset of the Router. 

@Rehman If you do not have too many personal settings in your router, I would recommend resetting the router as well.

But before try 8.8.8.8 as DNS server (which is the Google one)

The sudden change in behaviour could also be the result of a " Verschaltung ", which essentially means a mix up of the connection wires. This does sometimes happen when a new customer gets a new landline connection and a technician has a bad day... 

Thank you for your support! The Google DNS didn't solve the issue but the factory reset did.

I truly appreciate all the tips, and will be happy to buy you coffee if you're ever in Munich. 

Sorry, I was on the phone with the Customer Service and could not answer earlier!

I updated my router myself with the mentioned firmware after I failed to make it work yesterday. My DSL was set up in mid July and has been working all fine until yesterday. There was no change in any settings except that I noticed afterwards that my landline is reported be Offline but my router shows the Internet and the WLAN fine. It is quite weird that I can access some websites and can't many others.