Maybe resetting the SMC (System Management Controller) could help... at least have a try.
If the battery is nonremovable
- Shut down the Mac.
- Plug in the MagSafe or USB-C power adapter to a power source and to your Mac.
- Using the built-in keyboard, press Shift-Control-Option on the left side of the keyboard, then press the power button at the same time.
- Release all keys, then press the power button again to turn on your Mac
If the battery is removable
- Shut down the Mac.
- Disconnect the MagSafe power adapter from the Mac.
- Remove the battery.
- Press and hold the power button for 5 seconds.
- Reconnect the battery and MagSafe power adapter.
- Press the power button to turn on the Mac.
The LED on MagSafe power adapters might change states or temporarily turn off when you reset the SMC.