Why won't my battery charge?

So my MacBook Pro battery has been dead for awhile, but as long as I kept it plugged in I was still able to use the laptop with no issues. The other day, the computer was pulled to the floor (about a one foot drop). Everything seemed fine, but about 30 seconds later it shut off. I realized that the AC adapter was no longer giving power to the battery (it won't startup with the power cord plugged in and no battery, either). I tested another AC adapter and still no luck. Is this a logic board issue, or a problem with the MagSafe board?

Extra note: when the power adapter is plugged in, the light on it is yellow for about a second, then turns green to indicate a fully charged battery.