Apple ID not working in App Store I've suspected this for a while, but have proven it for myself by keeping an accurate track of my Apple ID and Password, having written them down + kept a log on another system. 

I went to the App Store to download the latest macOS Sierra update. While the auto updates worked well, signing into the App Store with my Apple ID did not work. 

I successfully logged into https://appleid.apple.com with the same password. I re-checked all my details. I then changed my password in my Apple Account Manager at the above url and re-entered it in the App Store after I shut the App Store down and reopened it. However, it would not let me enter with the new (or old password).

Obviously I am perplexed, frustrated and annoyed by this.

Does anyone have any suggestions on how I can address this?
Just a thought but maybe its signed in already on another account and needs to be signed out first. On the Store menu make sure that you aren't already signed into an account and if so sign out and try signing back in. It may work then again it may not. Just something you could try.