Recently my family went away from home for two months. While preparing to go, we left my wife’s Macbook Pro at home and got a bit of a nasty surprise when we returned. The Macbook pro wouldn’t start at all unless plugged-in. And then it showed that battery was not charging and its charge capacity is 0 (you can see this in System Information app). And the green indicator on the MagSafe adapter never went to orange (charging light), even after we left it overnight.
I then recalled similar account by Dan Benjamin - he also left a Macbook untouched for several weeks. The battery discharged so much that it was impossible to kick-start the charging again. He eventually had the battery replaced with new.
The recommendation is that, when you know a device will not be used for prolonged period of time, to remove the battery out (and that charge capacity should be about 40% at that point). In newer Mac portables though, battery is not removable (at least not without opening the case). Thus I assumed that this must be something Apple has thought about. A quick search offered a possible solution:
Unplug the device and all the peripherals.
Hold Ctrl + Option + Shift and Power button for 5-6s, then release them all.
Plugging back in, I was relieved to see the orange light. At first, it showed that charging would take 10h :) but after 5mins or so it got down to normal 1.5h-ish.