MacBook Air Won't Start Without Battery Pull?

My Macbook Air is misbehaving. It will operate normally, sleep and wake up properly, and reboot normally.

However, when the battery has drained or it is shut down, it will not start back up unless I disconnect the MagSafe and battery, hold the power button for a few seconds, then reconnect both. Afterwards, it boots up normally. Everything is fine so long as it is not completely off.

When it's turned off, the MagSafe indicator will be orange usually, but when you hit the power button it turns green and the machine does nothing until there's a battery pull.

P.S. SMC resets via the keyboard do not solve the problem, but do seem to occur (MagSafe changes color).

As I understand it, a battery pull+power button press constitutes a manual SMC reset? If so, why wouldn't the keyboard one solve it?