The problem is with the BMS (battery management system) inside the battery pack (--> http://en.wikipedia.org/wiki/Battery_management_system
If an unsafe state is detected, the BMS shuts down the battery to prevent it from severe damage (fire, etc.).
Some people manage to "repair" the BMS by going through several charge and discharge cycles but this doesn't always work.
A few years back we've played around with some cheap lithium polymer battery packs without BMS.
On heavy discharg load around 50% of the cells caught fire.. (Well, we were building an electronic car for the formula student, but the concept is the same
If you send your phone in to Sony, in most cases they don't change the battery, they just reset the BMS.
This problem can occur with all modern lithium batteries, depending on the BMS thats used inside.
I'll post here if I find a way to reset the BMS for the ZL battery, but I don't think it's that easy..
And still, you would have to open your device and connect the battery to a small microcontroller (if someone has programming skills, it might work with the Arduino board..?!?)
Depending on where you live, it can take very long (2 months plus) until you get your phone back.
You might think about replacing the battery yourself.. You can find them on ebay and several battery suppliers online for around 35$.
Here you can find the service documents: http://forum.xda-developers.com/show....php?t=2516874