2011 Air Battery Not Charging

Hi. I see that this question has been asked several times, but many of us have not found a solution, and each unique case is worth a try...

MBA is over 4 years old, have noticed the fan running more often lately, but no other issues.

Left town for a week and left it unplugged. Upon return, plugged it in and was streaming a ball game, and made a comment that it was weird the AC charger showed a green light. I don't remember what the power percentage was, but did unplug it at one point and it kept running.

Next day, the charger indicator stays green, screen indicator shows (Not Charging) and computer shuts down within seconds of being unplugged.

System shows battery cycle count: 593, condition: normal. It recognizes the charger as connected, but not charging. I have tried another plug and get the same result, so I don't think it's my plug. I've tried the SMC reset every way possible (plugged in, unplugged, etc.) to no avail.

Can a battery be bad even when indicates normal with a low cycle count? Maybe just from age?

I live hours away from an Apple store and would hate to give them more $$$ if I don't have to.

Who's got the golden ticket?! I appreciate your time.