Sadly, your logic board needs repairs. What has happened is the power control logic MOSFETs have failed. This often occurs when a knockoff MagSafe charger was used when the battery was in need of replacing.
There is nothing you can do here your self unless you have the skills to troubleshoot the logic board and have access to the needed tools and parts.
Do you have a local Mac repair shop? If not you may want to look at getting a replacement logic board. You will also need a new battery and a real Apple MagSafe charger (directly from Apple only).