Ever since my daughter was 3 years old we came across a game series called Putt-Putt... its a point and click adventure with basic logic problems. Your child only need be familiar with the very basics of using a mouse. There is nothing in it that a parent would disapprove of. If you're looking for a game for your child that doesn't have hitting or violence of any kind...this is the game...or game series.

My daughter is 6 now and still loves it...even though she is tearing through it much faster :)

Cheers