linux - 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

Answer

If you are comfortable opening up the laptop, you can look at the PCB near the power plug and look for any thing that looks burnt. You might be able to see something with a flashlight and looking close in the plug but I'd take it apart carefully.

It's possible the AC adapter may have been damaged by the power surge. No way to test except A) attach AC adapter to a known working laptop of same make and model, B) use a voltimeter when it's plugged in if you know what you are doing (I don't), or C) swap in a known working AC adapter.

It's possible the battery may have been damaged by the power surge. No way to test outside of the laptop except A) put it in a different, known working laptop, B) use a battery tester, C) swap in a known working battery.