Report Offensive Message

If the line/enable password is missing, how would you log into the router to change the config register?

The correct procedure is to determine the password recovery process on the Cisco web site, for that model.

Typically, on a router, bounce it, and issue a break sequence as its booting, to enter ROMMON mode. The config-register 0x2142 can be issued there without knowing any passwords. Press I to reload, and after it boots up, you'll be prompted to enter the configuration menu.