It sounds like you may need to make sure all of your LED sticks are completely "seated". Image below. Look for the last LED stick in the array that is working, and try to wiggle that one around to push the LED stick into position.
If that doesn't flare all LEDs in your Cube on, it's possible that one of the LEDs on the last working LED stick has blown. In this case, try to replace that LED stick and the stick before and after it in the array with the spare LED stick that should have come in your kit.
If those steps don't work, please email me at smf [at] lookingglassfactory.com and I'll make sure to get you back on your way to Cubing!
-Shawn, Looking Glass