I agree it sounds like a hard disc problem of some kind. My first thought is a bad connection between the disc and the motherboard, or maybe a problem on the motherboard itself. However that's just my limited experience talking, it could equally be the hard disc starting to die - which would be better news because hard discs can usually be replaced easily.
Since it boots from CD reliably, can you stop using the hard disc altogether and boot from CD every time? A lot of the live distros include tools to make customised live CDs, so you could burn one with all the tools your granddaughter needs, and give her a USB stick (or some Dropbox-like service if it's lacking in USB ports) to store her documents.