It sounds like it could be a few things. First, your battery could just be drained. Have you tried charging it? If so, does it show as charging when plugged in? If it doesn't, then try a different charger cord. You should also try your cord on a different device to see if it is good.
If it shows as charging, or does after using a different cord, then you should check to make sure the power button isn't 'stuck'. It happens. Press and hold the power button down for about 20-30 seconds, and then let go. Wait about 30 seconds and try powering it up again.
If that doesn't work, the next step is to try and reboot the tablet. This can be done by locating the small pinhole located inside the tiny door where your SD card (and possibly a SIM...