My brother gave me a Nexus 7 for Christmas 2012.  The first time it charged really fast and yes, I know that's because it had no content on it yet.  . But every time I turn the device off and charge, it seems to take a really long time.  It actually doesn't seem to charge past 43% even when left on the cable into the wall socket all night.

I charged it today for eight hours, turned off, and it only went up 10% charge to 36%.  I have Checked under apps to see what could be draining it, as the battery also goes down VERY fast, but can't see what it could be. Only six apps have been installed.

I noticed that under Battery, Screen says 78%. Is that normal?  Everything else under there appears to be under 5%.  Given I've only had it just over a week, what could be wrong with the Nexus?

I also wondered why it can't be charged when the Nexus is on, like other devices can?