This sounds like something malicious to me, especially given the Admin password being changed. If the DNS server is changed to something malicious then it allows an attacker to redirect you to different websites. Digital Ocean and BHost just rent out servers, anyone can rent one to host whatever they want (including malicious DNS servers).
I would completely reset the router (after noting down all your connection settings.etc) and set it up again from scratch setting the Admin password to something secure (and disabling remote management if there's an option) - If the router has been used with the default admin password and it allows people to connect to it over the internet it is possible that an attacker has been able to log into it and change the admin password/DNS server. It may also be worth updating the firmware on the router if a newer version is available to ensure that is patched against any security flaws that may have been discovered in that model.
If you still have issues after doing this, you may want to look at just replacing the router, it's a pretty old Wireless G model, a better replacement won't break the bank!