Abstract: Someone forgot the admin passwords to a Cisco 1600-series router and you have physical access to the router.
You'll need to know the break key sequence for your terminal program, fortunately Cisco has provided a handy list: Standard Break Key Sequence Combinations.
Connect your computer to the router's console port, ensure your terminal software is functioning and configured properly (baud: 9600, data: 8, parity: none, stop: 1, flow control: none, com ports will vary), and start or hard cycle the Cisco's power.
Enter the break key sequence within 60 seconds.
ROMMON> confreg 0x2142
ROMMON> reset
..enter setup mode [yes/no] no
c1600# copy startup-config running-config
Set your new passwords.
c1600# copy running-config startup-config
c1600# config term
c1600(config)# config-register 0x2102
c1600(config)# reload
That's it.
