I found this on another site.I know you've done some of it but the other stuff might help,
First thing to do is an easy on, try to turn it off and on again. Do this on both your Moto G and your router, turn them off and back on again. This old trick very often will do the trick right away.
If the first step doesn’t work, get to your connection settings. Check Settings > Wi-Fi and press on your router to Forget network. Rescan and re-enter all details one more time.
If you find that the connection keeps dropping, try this move: go to Settings > Wi-Fi > Advanced. Try changing two settings, make sure to set the Keep Wi-Fi on during sleep to Always. Also make sure that you leave the Avoid poor connections unticked.
When you notice that Wi-Fi interferes with your battery life and causing it to drain excessively, go to Settings > Wi-Fi > Advanced and turn off Scanning always available.
See if you need to change channels. You may download the Wi-Fi Analyzer app to see how full or crowded it is.
You may also try changing your router’s other settings. Make sure that you have turn off MAC filtering or add your Moto G’s MAC address. This can be found in Settings > Wi-Fi > Advanced. Lastly, try setting a static IP.
