[Nexus 7 Q&A, Help & Troubleshooting] bftb0:
I was under the impression that that scenario is exactly the bill - the battery drains off to such a low voltage that the internal charge controller circuit doesn't work correctly at that low voltage, even when you put the device back on the charger, so you are stuck with a not-dead unit that won't turn on, and also won't take a charge. (But that hardware isn't dead - you just need a partial charge on the battery to get the charge circuit to start working again.)

The only recourse really is to get a *small* amount of charge on the battery by some means other than the built in charger, and then reconnect the battery to the tablet and put it on the charger to complete the charging.

There are disassembly instructions on here that take you through the steps necessary to get to the battery connector (it detaches and has a short run of wire between that connector & the battery so that should be convenient for attaching the battery to something else without removing the battery from the tablet). Use the search functions.

If you can borrow a voltmeter, the symptom will be obvious: a very discharged battery will have a terminal voltage around 3.0v (maybe less). Under normal conditions the battery voltage will rise to about 4.05v when fully charged (measured when disconnected from the charger) and be somewhere around 3v when completely discharged.

Don't do anything stupid (there are examples of that on here too). The charger that you use needs to limit the amount of current to a reasonable value, say less than 500 mA. The battery can tolerate up to about 1.8 Amps of charging current but you should use something far more conservative than that for safety reasons. And you are only trying to put a small charge on the battery (not completely charge it) so you don't need to use the fastest possible charging rate anyway.

Something incredibly cheap would be a USB cable (with the micro-B connector cut off) and a 1/4 watt, 100 ohm resistor connected to the positive supply line coming from a 5 volt USB wall wart charger. Even if the battery was a dead short, only 50 mA of current would flow and the resistor wouldn't burn up. If the battery was good but heavily discharged, you'd only be charging at a 20 mA rate - that would put a 10% charge on the battery in ~30 hours.

If you initially measured the battery and found it had a voltage of 2.5v or higher, you could use a 22 ohm, 1/4 watt resistor safely and charge the battery 10% in only 8 hours or so.

You can charge faster by using a resistor of a higher wattage rating, but 1/4 watt size are readily available and cheap.

The equation for power dissipated in the resistor is

P > V^2/R or

R > V^2/P = (Vs- Vb)^2/P

So for example in our case with Vs = 5, Vb = 3 and a 1/4 Watt (P) resistor, we would get

R > V^2/P = (Vs- Vb)^2/P = (5-3)^2/0.25 = 16 ohms.

The "dead shorted battery" worst case would be Vb=0 or

R > (5-0)^2/0.25 = 100 ohms

(so you can see where the numbers came from)

Anyway, that's my recommendation

- disassemble to the point of exposing the battery connector

-disconnect battery from tablet

- put battery on simple & safe charging circuit (+ terminal to resistor to + terminal, and - terminal to - terminal)

- let it sit for a while*

- reconnect to tablet and finish charging

- profit

* if you leave a live circuit unattended, even if it is only a 5v circuit, please please no exposed wiring or loose connections. Use tape and plastic straws for temporary insulation... or shrink wrap if you prefer a neater look.