Is it the power cord or the battery?

My roughly 6 year old MacBook won't take a charge now. I've replaced both the battery and the power cord in the past two years or so, I believe, and all of a sudden it's dead. There is no charge indication on the cord so that makes me think the cord may be the culprit. On the other hand, just before my MacBook died the battery indicator said 85% but it did show that I was running off of the battery and not charging. Any thoughts?