Welcome to the forum!
I once had this exact problem. ADSL single-box routers that try and guess whether or not to use PPPoA (right answer) or PPPoEoA (wrong answer).
The right answer if you are using a BT-based service provider, unless you have no choice for some reason, is always PPPoA VC-MUX (MTU 1500) and the DNS Settings will be given to you automatically. Or you can set the DNS settings up by hand, to 8.8.8.8 / 8.8.4.4 or ask your ISP.
Your ISP may be using their own kit rather than BT’s machines that go ping in the exchange though, a so-called LLU ISP. If so the above does not necessarily apply and different protocols and setting may be in use.
That’s why we have to know which ISP you are using. I realise it may possibly be an embarrassing choice, but we will in that case be kind.
My problem was I think something to do with a fault in the ISP’s (Demon’s) equipment or BT’s kit and was temporary. After a short while detection went back to normal.
When you say DNS symptoms, I take it that you can’t browse the web but you can ping numeric IP addresses and you can fix things by setting the DNS server values up by hand either in your router or in your own machine?
If you do get DNS problems you may well be better using 8.8.8.8 (Google) or OpenDns’s very fast servers, or 1.1.1.1. These are all fast and extremely reliable as there are a lot of them distributed all over the place intelligently, many hiding behind ‘two’ addresses in fact. And since some ISPs’ servers are crap you could be better off using these than the ISP’s own, never mind problems with auto identification of their addresses. An ISP’s DNS servers that are of good quality will always have the advantage of proximity.