Welcome to Android Central! The 1st generation Nexus 7 doesn't have a rear-facing camera, while the 2nd generation does. If you were able to open up the tablet easily and manipulate the battery, you probably have a 1st generation.
The possibilities include a failing battery, a broken charging cable/plug, or a broken charging port. The easiest thing to try first would be another charging cable/plug. If that doesn't help, then you could look into a replacement battery. If a new battery doesn't help, then you could look into replacing the charging port, or if you have the 1st generation Nexus 7, trying to find one of the official docks, which charges via the pogo pins (those 4 contacts along one side of the tablet).