Answer to "What is the name of the joysticks things?"The thumb sticks connect to the circuit board. It would be way easier to completely replace the whole circuit board.
Answer to "Shift key not working"Plug in an external keyboard, do they work now? If no, try the steps below. Go to Control Panel then look for Ease of Access - Click on Change how your keyboard works. - Uncheck where it says Turn on Sticky Keys and click OK. If this doesn't work try checking the keyboard language if set correctly. - Go back to Control Panel then look for Region and Language and make sure all tabs at set to the United States. - Click Apply when a change is made then try your keyboard again. If these tricks don't work, you will need to replace the keyboard.