If your battery level is going down even if you are plugged into your computer and if you are having trouble doing the backup, I suspect there might be a problem with the connection between your iPad and your computer.
Even though your iPad shows "Not Charging" when it is plugged into your computer's USB port, it really is charging, but very slowly and your iPad definitely should not be losing battery power when plugged in.
You might try doing a system reset by holding in the Home button at the bottom of the screen and the Sleep/Wake button on top at the same time until the Apple logo comes on the screen. Then you can let go and let your iPad start up normally. This seems to cure a lot strange problems! After that, then you can try to update.