Battery issue with Macbook pro retina
The top case (or Upper Case Assembly) is essentially the case that contains the keyboard and trackpad. In some models, when replacing the battery, Apple will replace this as well.

In terms of other ways around your problem, you could try resetting the System Management Controller (SMC) to see if that has any impact. To give this a try, follow these steps:


Shut down your Mac
Unplug the power cable from your Mac
For 10 seconds, press and hold at the same time the shiftcontroloption keys (on the left side of the built-in keyboard) and the power button
After 10 seconds let go of all keys and the power button 
Plug in the power cable
Turn your Mac back on with the power button.