Nexus 7 (2012) won't charge or start after a series of problems
Looking at your issue related to battery and charging (which may not be the sole cause- I am not familiar with Nexus devices)


Since you barely used it for an year, it would not have been charged either and the battery could have discharged to very low levels. Li Ion batteries have a protection circuit that kicks in when the discharge falls below a certain level. It requires certain current to be applied to it before charging can happen. This is called "Boosting". How to awaken sleeping Li-ion explains it. Fix: Nexus 7 Refusing to Charge, Try This Trick mentions steps getting into the bootloader to revive it



  
  Plug-in your dead N7 to a wall charger. (Jump immediately to step 2.)
  Immediately after plugging it in, press Volume Down and Power at the same time.
  Once in the bootloader menu, use Volume Down until you see “Power Off Device.”
  Choose that option with the Power button.
  Once your device is off, unplug the charger and then plug it back into the device.
  You should now see the battery meter  with your device returning to life.
  



You could also try to change the charging cables- I would suggest is to use a 20/22 AWG cable for charging (if you don't want to buy, look for a short thick charging cable-it may help). See answer here for my details. Nexus 7 is more choosy: It will stop charging if voltage levels drop and resistance comes into play again. Google Nexus 7 Charging goes into details and says



  Nexus 7 will stop charging if the input voltage is less than the internal battery voltage plus 0.2 volts.



There are other drastic methods, which you could try if you are comfortable, involving jump starting