Hi, I'm Pete. Welcome to JustAnswer! I'm reviewing your question now, and will post back with your reply ASAP.
Can you try connecting an external keyboard to a USB port on the Macbook Air and see if that lets you logged on?
Once successfully logged on, we can work on carrying out any repairs...
Ok, so the problem is with the mouse and not the keyboard - are you currently using a wireless mouse? If so, check the batteries in it. Try replacing them then check if the mouse works again.