Well it sounds like the device hasn't charged/isn't charging and that is why it isn't turning on.
First you need to make sure your cord is actually working. If you can try using it on another device, or try using a different cord on your tablet. If the cord works on another device, then your device is the problem. If another cord works on your device, you know the old cord is the issue.
Also you can try checking the button to see if it is stuck. The outer button is just a kind of cover for the actually inner button that you are pressing down. If the button is stuck, it won't let you turn it on and it probably wouldn't charge either. You can try checking this while the tablet is closed (pressing the outer button a lot to see if loosens...