Hi there Bev and welcome
What you need to do is on your new computer install Garmin Express and sign in with your Garmin accounts in order to continue the updates.
To do this, on this new computer, download the program from here
Install it and then open it, sign in with your account and you can then do your updates as you did before.
I can also do these steps for you, and have made a request via Additional Services. This is optional, and if you choose to do this, I can, with your permission, remote into your computer while you watch and do all these steps (and deal with any problems that arise during them) for you. Or if you do not choose to take this service, we can continue here. This is no problem at all. Just let me know please.
Else let me know the results please.