Open an elevated command prompt (type "command" in search, the top result should be command prompt, right click and "run as administrator").

Type slmgr /xpr

The result will tell you if you are activated, what version of the OS is activated, and how long the activation is good for. "Permanently activated" is what you want to see.

Type slmgr /dlv

You will get a whole bunch of detailed information about your Windows license.

If you aren't activated, you can try slmgr /ato, then slmgr /xpr to see if it worked. If it didn't work, give it a few days and if you still aren't activated, call Microsoft:

How to Activate and resolve common Product key issues in Windows 10 - Microsoft Community

This works at least for Windows 10 and Windows 8/8.1 and I am 99% sure for Windows 7.