MacBook Air's battery doesn't charge, Service Battery state, but only 400 cycles

Yesterday everything was fine with the battery in my MacBook Air 13'' 2012 (2 years old). It was lasting for 4-5 hours like new. Today, all of a sudden, the battery has stopped charging at all (I have only 40% left). While the power cable is plugged in, its LED doesn't indicate any colour. I rebooted the system, no difference. In System Info I have:

Cycle Count: 409 Condition: Service Battery

I heard that the lifetime of the battery should be 1000 cycles. I didn't update any software recently.

Does it all mean that the battery is dead? Or maybe there is a way to conquer it? Thank you!