Laptops don't like to be moved while powered on because doing so can ruin the hard drive. I don't know if that's why that screen is turning green or not, but your granddaughter needs to be very careful about that. Re the touchpad, what I have done on my laptop is to disable it and get a real mouse. They come in varying sizes, cordless and corded, and I find mine greatly preferable to that touchpad.
My granddaughter has an Aspire 3810tz and has been having problems since it was about 18 month old.
Firstly, the screen goes into green pixelation if the lid is moved and then goes back to normal if lid moved again.
Secondly, the touchpad is faulty and the left hand side appears depressed all the time and any text on screen is highlighted and won't react to the pad. It does work OK using a mouse though.
Any ideas please regarding what the problems may be and if they can be rectified cheaply?