Bottom of touch not working
I would try a restore and also run the battery down all the way until it is dead. If those do not work you will probably have to replace the screen on the iphone. You can get it done through Apple or if you want to do it yourself here is a link to a parts reseller:
They also have videos on how to take apart the entire iPhone so you can try and replace it yourself, but let me warn you (because I've taken a few apart myself) it is not as easy as they make it look in the video.