A search pulled up that the code requires a thermal reset. This video shows the power switch being used, along with the GFI test button on the pump cord, not on the pump itself. Here's the link: https://www.youtube.com/watch?v=isgLwdtb...-E
This is a common issue with the joysticks on the controllers. Over time and from use there is a little clip in there that wears down and you start to get stick drift. I have it on 2 different ones, only both are in the left stick for me. Always upwards though. There are some supposed ways to try to fix this posted online, but none of them fixed mine (anything from pressing hard and moving in full circles to alcohol & cotton swabs to remove oils & dirt - none of which solve the underlying problem). You can try to take the controller apart with a T-8 bit and spudger and see if anything is broken, but it may or may not be something you want ot get into.
If the screen shows the battery indicator when you plug it in, then either the battery is bad or your charger is bad and the phone is not charging properly. As staff at a GNex forum, this is only the second time I have heard this, and the following solved the other problem: I would make sure the charger is the one that came with the device (I have a few LG micro-USB chargers that fit, but do not charge the device) and wait about 5-6 hours to make sure it charges completely. If it still will not power up, try another battery. (the GNex uses a battery that includes the NFC antennae right on the battery so if you plan on using that, you will need that in the permanent one) If a new charger and battery do not solve the problem, it may be an issue with the wiring to the battery/charging circuit. A replacement may be required.