App Store on OS X broken after system restoration from backup

There are several Options you could try in order to identify the source of your troubles:

• create a new User and try to access the AppStore with your current ID (or a temporary one). If it works, the Problem lies within your User-Profile and not the OS. If it doesn't, the Problem is located in the OS (or the Drive itself).
• OS & User-Profile: try clearing out the Cache files, either manually (see f.e. StackExchange Article here) or use the freeware 'Onyx' (my preferred method)
• OS: Check the Harddrive and the File System Permissions with Disk Utilities.app (found in /Applications/Utilities). It is possible (but not liklely) that your HD or Filesystem is defective/corrupt.
• User-Profile: go to ~/Library/Containers/ an move the Folder com.apple.appstore somewhere else, f.e. the Desktop. Try starting the App Store again.

Try these and if it doesn't work look in the console. perheaps there are news error messages there.