You can login to a computer with a domain user/pass when not connected to the DC. Of course you will not have Network Admin rights but if you have local computer admin rights you are good to go.
They way to check is just create a new local computer user. If you can create it and assign admin rights then you are a admin. You can also check in users if the account you use has admin rights as well.
With this said a fresh install would be nice. I am a bit surprized that they sold the computer without wiping the hard drive first. If it has a sticker with the key you would be good to go for a reinstall. Just need to borrow a copy of the correct OS.