With most button-activated e-cigarette kits, the key to locating a fault lies with the battery button.
If you have checked that it is turned on and the button illuminates when pressed, then this usually indicates that the battery is not faulty and that the issue lies elsewhere. The problem is likely to be either in the connection to the clearomizer or in the clearomizer tank itself (where your e-liquid is held).
If your battery is fully charged and is failing to turn on (ie the battery light simply doesn't illuminate no matter how many times you press it), it may have a fault. Batteries have a limited lifespan, but you can check here if yours is still under warranty.