The volume and power button together is to do a "Hard Reset". That won't help if it won't turn on.
When you plug it in, does it charge? If you see no signs that it is charging, try a different charger cord. If it still shows no signs, and you know that second cord works for sure, then you may well need a new battery. (and yes tablet batteries can be changed, they are just a pain to do.)
If that is the case, first check if the device is still under warranty. If it is, contact the manufacturer about a repair or replacement.