The battery for my Lenovo Yoga 2 13" is unresponsive. I've decided to switch it out. How should I go about doing this?

To replace your broken screen with a new one, you can follow this guide.

You can use this guide to learn how to access the fan through the laptop's back panel.

Before replacing a hard-drive it's important that you create backups of any important files. Move those files onto an external drive or create a restoration disc for safe keeping. Now you're ready to access the hard-drive via the laptop's back panel. After you remove the old drive, take the next steps on this guide.

Your touchpad might not be working because it could be disabled. Check out this troubleshooting guide to figure out whether you need to check underneath the touchpad to remove any debris, or if you need to replace it entirely.