iPad will not work, blue screen, nothing is working

I recently purchased an iPad 4, 32GB with wi-fi + cellular two days ago and last night, the iPad shut down for some reason. I was cleaning the screen with a microfiber cleaning cloth while the display was turned off, went on my computer for a few minutes, and went back to the iPad to find that it would not turn on.

I tried a hard reset, which did not work, and I also tried to connect it to iTunes, but iTunes would not read the iPad. Eventually, I plugged in the iPad to charge and left it alone for the night.

This morning, I woke up and tried a hard reset again, which worked. However, after turning on the iPad, the display soon turned blue and the iPad shut down, automatically restarting. The iPad display then worked fine, but then I experienced troubles with the home button's responsiveness and after turning the display off, the iPad powered off and currently, will not turn back on. Nothing I do will turn the device back on.

Are there any other quick fixes out there that I have not tried? Is this a hardware problem? I intend on bringing the iPad into the store soon, but I wanted to see one last time if I could try and fix it on my own.