You may be able to keep operating your camera even if the screen breaks. In this case you don't have to buy and install a new screen. If you can't use your camera because of your broken screen, you'll have to replace the screen. This part of the troubleshooting guide should help you with your problem.
All batteries suffer from shorter battery life when they get older. The battery isn't really malfunctioning when this happens, so you don't need to replace it. But if you need your camera to last longer between recharging, you may choose to replace it. This part of the troubleshooting guide should help you replace your battery and extend your battery life.