Computer won't power on with battery or power adapter

My laptop, for a period of months, would not start back up after being shut down for a period which ranged from hours to as long as a week sometimes. Now it will not start up at all. I've tried all the basic steps. The battery claims to be charged and healthy, but it won't boot from it or the power adapter, together or seperately. The power adapter shows a strong green light, but it seems like it's still not getting power. My question after reading on this a little: does this sounds like the MagSafe board needs replaced or is this more likely going to be a logic board issue? I don't think trying a new power adapter would help because it won't boot from the battery, but I guess it is possible that both failed?