[Galaxy Note 10.1 (2014 Edition) Q&A, Help & Troubl] lectricpharaoh:
This past week, I purchased a 2014 Note 10.1 off Craigslist. I did check it out before buying it, and the device is in pristine condition, including the screen. It booted fine, and I went partway through the setup (the guy had factory reset it) before closing the deal. It is the wifi-only model, 3G RAM, 8-core Exynos version. It's white if that matters. ;)

Anyways, a while later when playing with it some more, completing setup, etc, it just died on me. I wasn't home, and didn't have a place to charge it until I got home, but just figured that despite the device having said the battery was 99% charged, the guy keeping it unused for a long time might have thrown off the battery calibration. My understanding is that a Li-ion battery has one or more cells, plus circuitry that protects against overcharging and undervoltage conditions, as well as tracking the current charge state. With lengthy non-usage, the circuitry's idea of the current charge can get out of sync with reality, so I figured a few charge-discharge cycles would get it back in shape.

However, the situation after I got home turned out to be a little more complex. If I plug in the device to a power source with enough current (like the charger it came with, or my 2.1A USB outlet by my bed), it will run just fine while plugged in. However, upon unplugging, it would die quickly. Naturally, I assumed the battery was probably shot, so resigned myself to spending $50 on one. This is where it started to get a little weird. It seemed that when I booted into either fastboot or Odin mode, it would stay on much longer than normal, while unplugged. I'm talking hours, rather than between several seconds and several minutes while booted into the OS proper.

This lead me to believe that perhaps it wasn't my battery itself, but rather a glitch in the OS that was causing it to shut down. When I say shut down, I mean an immediate full-off state, not a nice shutdown or one preceded by low battery warnings. It just clicks off like a light that's been turned off. However, trying several different firmwares, including a couple custom ones, has not yielded any improvement. The issue remains.

The device was stock 5.1.1 when I bought it. I tried flashing KitKat (various images downloaded from SamMobile), but for some reason, it would still say it was running 5.1.1. I tried xKat, as in this thread. That results in 4.4.2 with the associated customizations, but the shutdown issue remains. I tried CyanogenMod 13, as instructed here. It works fine, notwithstanding the same issue. In between the stock firmwares (pushed to the device with Odin) and the custom ones, I would do a full wipe through TWRP.

I've popped the back off, disconnected the battery, waited a bit, and reconnected it.

Now my question: does anyone have any idea what's going on? If it's a dying battery, then why does the device say it's got a nearly full charge, and why no low battery warnings? Why would Odin mode or recovery (TWRP now) seem to keep the device powered up so much longer? Sure, they draw less power, but hundreds of times less power? I doubt it. If it's some hardware issue with the chipset/motherboard/etc, then why does it only manifest when running on battery, or a low-current USB connection? If it's an issue with Android itself, then why does nobody else seem to have this issue (googling revealed nothing that matched my symptoms), and why did several different versions exhibit the exact same problem?

I really don't want to spend money on a new battery and wait a few weeks for shipping if there's something else I'm missing that could get my device functional for free and a lot faster.