The touch screen does not work on leapster 2

Turn off the Leapster2 and remove cartridge (if there is one).
Push and hold down the hint button (the one with the question mark) while the game is off.
Turn the Leapster on while still holding down the hint button until you see the calibration screen.
Push the "A" button to enter the calibration.
There will be a little plus sign. Touch it with the stylus and continue to touch the plus signs with the stylus until you return to the calibration screen.
Turn the Leapster off and then back on again without a cartridge. Login as usual.
If this does not work, then call customer service, depending on how old it is. I've had ours for over a year, and this still works each time.

We had the same problem within a couple of days of purchase and we were advised to take it back to place of purchase for a replacement. Not sure how long you have had yours though. Suggest you ring the customer support number and discuss it with them.