It would help a lot if you posted the model number of your HP Mini laptop since there may be differences between them that would affect the way we answer.
If your laptop has the capability to drive an external monitor, that would be the place to start; plug in a separate monitor and see if you get a picture. If you do, that would indicate a problem with your display, and if not it could be an issue with the graphics controller.
Try that out and let us know what happens.