Hoy to the sketchup website, log into your account, then go to plan settings, there your sketchup license will be shown, to the right of your screen it should say edit plan settings, click there and go to manage seats.
The OP has a Classic license so instructions for subscription don’t apply.
I would guess that the changed way SketchUp looks for an Internet connection is part of the problem. There has also been recurring problems with the older license management servers. @colin , What is the status here?
Is Trimble still working to fix this issue? I’m having the same problem migrating to a new computer, and the customer service representative said they are no longer putting efforts into fixing the 2016 license issue because they consider it ‘maintenance and support,’ and the time period for that is over. Thanks in advance!