App Store not launching
Since it is not clear what is not working I recommend following steps:

Trash that Dock Icon, then go to Finder applications and start it from there.

Or use iTunes to access it.

Once running right click and keep in Dock.

Possibly just use Disk Utility and restore/Repair preferences settings.

If it still not working, try with new preferences files.

Find them in  ~/Library/Preferences/

com.apple.storeagent.plist
com.apple.appstore.plist


Quit all applications on your Mac, delete the two files above, and reboot your Mac.

If still not working use cmd+r to restore your OS installation..