OK, I played your save. I think it's corrupted because you should have 'clear' hints, and not a line of squares as you have when you over the mouse on the stars.
Anyway, to get The Babysitter #1 started, start a contract. Begin to work on it. The first night, play LOL.
Second day work on the contract. In the evening be in the livingroom and skip time. At some point you catch Amy playing (attached is your save at this point).
The following morning go talk to Charlotte about babysitting. From then on go through the 2 events.
Follow the walkthrough (link at the bottom of my signature) to have the hints that are not ingame in your save.