Cannot sign into Apple Mac AppStore
It seems that you may need to reconfigure your computer's iCloud. You can achieve this by reinstalling OS X. Then it would allow you to set up your iCloud account from start out. Before beginning, I strongly recommend you backup your computer just in case something goes wrong


Restart your Mac
When you hear the start up chime, hold Command ⌘+R
Click "Reinstall OS X"
Follow the instructions listed


If that doesn't work, you may need to fully erase and restore from backup.