If nessessary you can use an admin password retvial software. But the company may be alittle upset if you do. Your best bet would be to take the laptop to the IT shop of the company, if you have one, and get them to do the update for you.
Now as far as using a router, if your going to use another computer to try and connect into the laptop via a router, your still going to need the admin password. If your going to use the router to connect directly to the broadband then to the laptop you should be able to do it. But it is going to need to create a connection to the router, and if this function is locked out as well then there is nothing you can do.
Another thing to think about is DHCP. Has the NIC that your connecting to the router been configured before? I would think that from the sound of the Boots company, that it is locked out as well. However if it was configured for DHCP, and your router is prior setup for DHCP, then yes you can plug any DHCP enabled device into that router and connect though its connection.
Life is like a womens underware. Hard as hell to get into, but fun as sin once you do.