A few days ago, I went on vacation and unplugged power cable from my MacBook Pro 13' early 2011 and then I got back home, the battery was not detected by OS and didn't charge. I then understood that I had automatic startup configured and the laptop did power ON next morning then I was not at home. The battery was discharged completely.

I tried to restart, to power down and unplug power cable, I also tried to did SMC reset, but that didn't work.

What's the most reliable way to check the health status of the battery? - I want to replace it, but I want to be completely sure that this is the battery, and not something else.

Battery is about 3 years old and about 250 cycles.

The battery icon is the same as below: