I've seen the first part of that behavior before with updates, and while not exactly intuitive, it is normal. macOS is typically downloading and installing in the background, and the update screen won't respond until that is done.
However, you said you left it running for days. That doesn't sound so normal. I'm going to presume you have some sort of high-speed Internet connection (at least 10Mb/sec), and if that's the case, it's probably not your Internet connection.
However, If you want to see the progress of the download (if there's one going at all), look at the "LaunchPad" icon on your Dock. It will display progress bar below it when something is downloading and installing.
If there really is nothing happening, try logging out of the App Store and back in. To do this:
- Open the App Store
- Click on the Store menu
- Click "Sign Out"
- On the Store menu again, click "Sign In..." and sign back in
That will probably do it for you, but give it a try and see.