Try holding down the power button for about 30 seconds and then let it go. See if it turns on. If not hit the power button again (not so long) and see if it will now turn on. If not, then you can try the following.
1. If you feel comfortable opening up the device, and it isn't under warranty, check inside to make sure there are no parts loose, disconnected, etc.
2. There should be a pinhole on the tablet that you can stick something small (but not sharp, don't want to damage anything) info it and depress the button inside. This will do a "Factor Reset" and see if it allows the device to then turn on.
3. NOTE: Doing this will clear 'all' the data on your tablet, so it is suggested you not choose this option unless you have to, or...