How to remove very worn screws from my system?

So about a year back, my 3DS became faulty, as it began to suffer from the black screen of death, (wifi chip falls loose). After trying to unscrew it with a recommended screw driver, many of the screws were too tight, resulting in them becoming worn. After trying every trick in the book about using rubber bands and Blu tack, the screws became stupidly smooth. So I just decided to buy a new one, but now I need my old one fixed for my younger brother. Any possible suggestions?