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.
You can also try and see if there is a reset button on the tablet (it would be a little hole you can stick a pen in) press that, and then try charging. If that doesn't work, Try pressing the power button for 20 seconds and then try charging it. Sometimes, if they device is allowed to completely drain, then it doesn't like to restart without issue.
If it won't charge, even with a new cord, it could be the battery, which you would then need to replace, or it could be the port where the charger plugs in.
If it is either of these, and you feel comfortable doing it yourself great. If not, I suggest taking it to a tech to have them do it. Especially with replacing a port (if that is the issue) as it is usually attached to the motherboard, and then that would need to be replaced, if the port is the issue.