Basically underneath your laptop you should have to slider switches both need to be slided to unlock, once this done you can then unslide your battery, make sure you do not have your charger in at this point. Then once battery removed plug your charger back in and try turn on. If now you get nothing, chances are is your Asus power cable. So you need a new Asus charger. You can find a wide range of here: Asus laptop chargers
select the one needed and get one and hopefully end of problems for you.