Sadly, the earcup's contents weren't as plentiful as I had hoped. Housed inside are the lithium battery, noise-cancelling microphone, LED control circuit, and power/charging circuit.

In my case, I initially believed the battery could be the issue. I took a multimeter to the positive and negative connections and read the voltage just above 4v (it's a 3.7v battery), which means that it is holding a full charge. Quite unfortunate for my diagnosis.

After completing a visual inspection the circuit board for any signs of component failure (discoloration, burn marks, melted exteriors, etc.), it was time to look to the other earcup for answers.