I was having similar issues as many others where at first it seemed it just wouldn't turn on. One day I switch the plug I had it charging while it was plugged into the device and it turned on to the looping RCA screen. Then I left for work and when I came back home it was blank again. I hit the power and it would just go back to the looping RCA screen. So I started holding the power and volume buttons at the same time and eventually got to the recovery options and did these steps:
Select “wipe data/factory reset
Select “yes”
Go to “mounts and storage”
Select “format /boot”
Select “yes”
Select “format /system”
Select “yes”
Back out of that menu to the main one again and select “advanced”
Select “Wipe Dalvik Cache”
Select “yes”
And rebooted. It worked I got it and then the system asked if I wanted to update. I said yes, it failed with a dead android logo, restarted, and then I was getting all the same issues and I couldn't even get back into the recovery settings again. When I would push a volume up or down and power it would just flash white for a second and shut off. I played with every different option to get to recovery for about it hour and all of a sudden I get a message that update failed do I want to delete file. I say yes and I'm back in and working. For ****s and giggles I go to update again, it starts and fails again, but after a restart I get right back in with the same message to delete file. I then go turn off auto update.
So if you're having a black screen issue I would first try to plug in the device into another wall jack (or the same one but unplug and plug back in) while it's plugged into the tablet. That seemed to get things going. If that works to get at least a image on the screen then progress is being made. Let it charge up again just in case. Then hold the power for 10 seconds to turn off for sure. Then start trying the volume down and power button at the same time to see if you can get to the recovery options (there may be one that auto resets and another one where you have to do the options above). Don't do the update unless you're curious. Hopefully that works for you.
Right now I just cant get Youtube to play videos? At least I got this for free since it "didn't work".