Battery sort of died after a power outage

Battery sort of died after a power outage

So today the power went out and my laptop did a strange popping sound and
turned off even though it had like 50% battery (it was plugged in at the
time though). This has never happened before, it'll usually just switch to
battery and move on. Now it won't start if not plugged in and as soon as I
plug it out it shuts down.
$ acpi -V
Battery 0: Charging, 45%, charging at zero rate - will never fully charge.
Battery 0: design capacity 5616 mAh, last full capacity 5438 mAh = 96%
Adapter 0: on-line
Thermal 0: ok, 67.0 degrees C
Thermal 0: trip point 0 switches to mode critical at temperature 100.0
degrees C
Thermal 0: trip point 1 switches to mode passive at temperature 98.0
degrees C
Cooling 0: LCD 0 of 10
Cooling 1: Processor 0 of 10
Cooling 2: Processor 0 of 10
Cooling 3: Processor 0 of 10
Cooling 4: Processor 0 of 10
Cooling 5: Processor 0 of 10
Cooling 6: Processor 0 of 10
Cooling 7: Processor 0 of 10
Cooling 8: Processor 0 of 10
The battery was fine before. acpi confirms this - 5438 out of 5616 mAh is
pretty healthy for a 2 year old battery if I understand this correctly.
However, it says it's not charging and even though it's at 45% the laptop
doesn't use it.
$ cat /proc/acpi/battery/BAT1/info doesn't add any useful information,
beside a cycle count of 0, which is very odd. I've definitely used the
battery in the last 2 years.
So my question is this: what should I do now to pinpoint the problem? I
can grab a replacement battery off ebay, but I'm not sure whether it's the
battery or the laptop that's faulty.
laptop is lenovo ideapad y560 with ubuntu 12.04