Unless you're leaving some other info out, you can probably just put a fingernail underneath and peal up on the protector. There's a layer of plastic there so it should all stay together. Just prep the screen surface with the alcohol pad that comes with the new protector.
Did you just buy it? Chances are that the pins for the cartridge reader are bent/broken? Shine a light in the slot and see if this is true. There may be dirt or hair in the reader that would prevent it from reading games also. All ds models have issues with the pins breaking off if you're not careful when inserting games. You can put a new reader in if you're handy with soldering and small electronics. Otherwise it may be best to sell it as a repairable and buy a new one.