Air carrier Captain reported a ground gate delay to retrieve a Lithium Ion battery powered laptop from checked baggage. Flight departed after a long delay.

Narrative

Aircraft APU was MEL'd. Ground cabin air had been disconnected to start the right engine when ramp crew was instructed to stop by the ramp supervisor. It became known that a checked bag contained a laptop with a lithium battery. The bag was retrieved and the laptop removed. TSA agents were required for the laptop/bag issue. I again queried the ramp agent on intercom about starting the right engine and he replied that the ramp supervisor said no. I went out to the ramp to inform the supervisor that the cabin was getting warm and that I needed to get air to the cabin by starting the engine. She refused. I stated that the cabin needed air or the passengers would need to return to the terminal. She said that I should do what I needed to do. I stated again that the engine should be started and she said we were unable to start due to limited resources. Four to five ramp personnel were available and standing by but were waiting further instructions as the ramp supervisor had halted all activity to wait for the TSA. The ramp supervisor did call for ground air to be reconnected. The TSA agents arrived; explained what they needed to do; and waited. After a few moments; I asked why we were waiting; the ramp supervisor left; the TSA took the laptop to the passenger; and I returned to the cockpit. We started the engine; pushed back; taxied out; and departed. The ramp supervisor should have first come to the cockpit to advise me about the situation. At that point the ramp supervisor could have been informed of the APU MEL and the air requirement. The limited resources explanation was inadequate. If the ramp supervisor had specific concerns about starting the engine that is what should have been clarified.