If the mouse pad isn't even responding to your touch, or goes in incorrect directions, you may have a damaged mouse pad. Before trying to fix it, try restarting your device first. If that still doesn't work, then try replacing the mouse pad by following the HP Compaq NC6120 Troubleshooting Guide to get a start on replacing it!
Something that may cause the black lines may be out of date drivers. Try updating the drivers for the monitor. If that doesn't work, then the screen may be damaged and it will have to be replaced. Do try checking the HP Compaq NC6120 Troubleshooting guide for repair help!
A very simple and easy fix to this problem is to take out the fan, and clean the fan with compressed air. Alternatively, you can replace the fan altogether. For more help on this,check the HP Compaq NC6120 Troubleshooting Guide for repair help!