If the unit works on USB but not battery, double check that the batteries are clear of their plastic wrappings and that they're oriented in the compartment correctly. If you have fresh batteries on hand, give those a try just to make sure the original batteries aren't defective or depleted in transit. Batteries can also weaken if stored in low temperatures for long periods of time.
If you try both power methods and see no LED activity whatsoever, try performing factory reset on the unit. This type of reset can also be useful if you see LED activity but the sensor is unresponsive in other ways. If you're unable to wake up the unit, include it, or exclude it from your Z-Wave system, reset can help.
Don't close up and install the sensor until you've got it up and running - the back cover is secured with screws, so it'll be a hassle to need to keep opening the cover.
If the sensor is still unresponsive after trying all the above, please let us know! We'll be happy to help.