I agree with TechniSol, you should avoid simply connecting a battery. It is crude and dangerous.
I had an instance of the same symptoms where the Kobo appeared to be dead, the battery volts were zero and it wouldn't charge. It was almost impossible to connect anything to the battery connector without damaging it so I carefully soldered two wires to the other end of the batter leads where they connect to the battery board. I had to cut away some of the plastic film first.
I also made sure that the battery connector was unplugged.
I then connected a resistor is series with the positive to limit the current. 270 or 330 ohms quarter-watt is sufficient to limit the charging current to around 30 milliamps when connected to a 9 volt battery. I monitored the battery voltage and it rose above zero almost immediately. After a minute or so it had reached 2 volts which was enough for disconnecting the 9 volt battery and reconnecting to the main board. It then charged as normal and now works fine.
It is clear that the Kobo charging circuit leaves somewhat to be desired because it can get in to this lock-out situation.
Another underlying problem is the ease that the Kobo can be triggered in to an on state by actions such as plugging switching the charger on or off thereby leaving it in an un-noticed on state which which drains the battery.
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