If you are not able to log into the User Account for this license, then no. If your organization accidentally cancelled your authorization, they will need to fix it at the license server or give you the user name and password to do it yourself.

If you can get the old one back temporarily, you can try connecting to the internet, seeing if Deauthorize Finale is there in the Help menu and try that. Then log in with your new PC and try again.

Site and group licenses don't always work the same as individual licenses. I used to administer one for Finale about 12 years or so. With the current scheme, as Admin, I would be able to deauthorize as needed but I would not have given my users the user name and password. No, no.