Macbook won't turn on
Since you did not specify what  have you tried this is going to be a guess game:

1***Take the battery out and put it back in. 

That usually solves the problem of "oxidized" connectors.

You can try to clean the connectors but normally just in and out does it.

2*** try the power button, by pressing in rapid sequence or holding it for 10 seconds.

Since you just disclosed that when plugged in the battery shows to be charging, and before you said it is fully charged, so give it time and see if the charging light goes off.