Installing 10.9.2, "shutdown because of a problem", now Mail won't open and App Store won't work.

While installing OS X 10.9.2, my MacBook Pro suddenly "shut down because of a problem" (which isn't the first time that happened). Checking the Apple menu and "About this Mac" it says I have 10.9.2 installed. I tried to see if I could reinstall the update, figuring something went wrong when the computer shut down, but the App Store won't work, clicking on "Updates" or any other tab doesn't change the screen from the App Store icon in the center. Mail also won't open, which is what I ; I tried to see if I could reinstall the app, but I don't have the CD that the support page said I needed. It seems to be only Mail and FaceTime that won't open so far. How do I fix this?