Had almost the exact same problem. I had been without using my Nexus 7 because I dropped it and the screen cracked. During the time I waited for the replacement that I ordered via internet, it ran off of battery. When the replacement arrived and I finally changed it, I connected and it seemed like it had no problems. Then, when I tried to turn it on, it just booted, a screen came out saying "turning off" and it turned off. I decided to wait a couple of minutes, but it didn't work. I panicked too, I had been dying to finally get my screen and it seemed like it wasn't the only problem. Then I decided to check if the charging adapter had something to do because I lost the original nexus 7 one, and was using a Samsung cellphone charging adapter instead (that used to work). As I suspected, nexus 7 charging adapter uses 5V-2A, and the samsung one was 5V-1A. Checked around the house for another 5V-2A, found it and plugged my Nexus, it instantly worked 
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