We had a bizarre situation recently where our internet access went highly unstable. It was very patchy, with some website access being fine and other access being impossible. Interestingly, video streaming would work - but only after many attempts at getting it started. The logs on our router showed that the DSL was being disconnected very frequently (ie, every minute or so), so we assumed that there was a problem on the line or at the exchange. Annoyingly we had sold the router given to us by our internet provider, so we couldn't use that to see if our new router (installed a few months previously) was at fault.
Well, we tried another 3rd-party router: no luck. After an engineer had come out and improved our line (increasing the raw line speed from 40Mbps to 48Mbps) we still had the same issue. Our internet provider sent out a replacement router, and this still didn't fix the issue. When their only suggestion was to send out an engineer again, I almost flipped my lid and insisted that I speak to their specialist team. Fortunately the next person I spoke to immediately clocked what was going on: our DSL login was being used by someone else. The penny finally dropped: this was the person who had bought our old router! The technician very cleverly blocked that router from logging in as us, and the problem was immediately fixed.
Now, an amateur mistake like this - leaving our login info on the old router - would not normally have caused a problem. However, our internet connection is on a static IP address, so the issues we had were caused by both routers being given the same IP address - and the ensuing chaos of inbound network traffic getting sent to the wrong router.
If we'd been on a dynamic IP (like most people do) then the issue might have gone un-noticed. So this is an internet health warning to you: if you have sold your old internet router, and don't think that you cleared it out first, get in touch with your ISP to check that your login is only being used by one router!