Is there a way for people to look up someone's Drivers License number on the internet for free?? I need this because I'm trying to register my car in my name and the person who I bought the car from has moved and I am unable to locate her and the DMV reuires this information to put the car in my name.

No, not free and very doubtful on the internet for most places, In fact in many states you will not even get this info.

But you should have a signed bill of sale, and a signed title. Why do you need other info?