The older DSTT's (the one without the indention near the microSD slot shown at the top of the "anti fake" page on the ndstt.com website) are glued shut and to look inside you have to force them apart, and then glue them back together once you're done. Luckily, if you have an older design you can tell if it's fake without opening it. It would have a gold dot near the microSD slot visible without taking it apart. If it looks like the older design and doesn't have a gold dot, it's just one of the older ones which are not fake.
If your cart has the indention near the microSD slot, it's a new design, and there's no way to tell if it's fake or not without opening it. But I believe the new design isn't glued shut (I think it just snaps shut). Someone please correct me if I'm wrong.
By the way, some are claiming that the 1.16 version of the firmware contains fake-killer code. It's possible that yours is fake and that the firmware killed it.
Either way, return it to DX, tell them it's not working, and make sure you specify that you want a REAL one in exchange.
-Bri