Close your browser, open SketchUp, sign in, then Alt-tab to see what applications are open. Is your browser now open? If it is open and apparently has a window that you’re not seeing, read this post and try something similar to retrieve your browser window:
If your browser isn’t open, or it’s open and has no windows, go into the Windows control panel, where you can set your default web browser. See what it is currently set to, and try changing that to Chrome or Firefox, or a recent version of Edge.