She keeps paying attention to you, treats you nicely and wants to impress you. But there are some girls that try to hide their feelings so they act rudely to their crush, so their crush won't have any idea that the girl likes him.
When you get rejected by a girl you learn from it and move on from them. You find another girl to have a crush on and to impress. She didn't really deserve you anyways. Remember friendships should keep lasting a lot better than relationships.
Okay, really? You can't impress her by being dorky...what a stupid question, you have to be funny or less dorky, unless you want a dorky girl in which case you should read her a passage from your favorite bug encyclopedia, hope that helps
First of all, if you use proper English then that can impress a girl. Secondly, you impress a girl if you just be yourself, if the girl can't accept that then move on and find someone new! Good luck! :D