|To clarify - you can connect to the router at least via wifi - or ethernet connection?|
Presuming so and you are unable to actually get onto the internet via your broadband service, then the user name and password you seem to be being asked for is the one that is provided by your broadband service - your (ISP). It is not factory set in your computer; but is separate and distinct and as I say provided by your ISP.
Is the router you have "yours" - or is it one provided by your ISP?
If the latter (provided by your ISP) then frequently the user name/password is hard coded into the router setup by your ISP. If it's your own router then you would have had to enter those details manually when setting up the router; and those details would have been given to you by your ISP.
What make/model is your router; and is it one provided by your ISP or not?
Have you tried simply power cycling the router; switching off completely, waiting a couple of minutes and then switching it back on.
What happened to cause the current situation?