what happens if you try to shift the brake lever? I'd disconnect the cable and see if it'll click then - that would tell you if it's the shifter or a cable/derailleur issue for sure.

If it is the shifter, take it to the shop and have them get you a new one under warranty. If it's the cable, you can do that yourself (but if you don't have cables and cutters, you'll have to go to the shop anyway).