Engine start was initiated using the onboard battery. Afterwards, following an initial unsuccessful start of the left engine, both engines were started around 9:53 a.m. But problems continued to mount as the aircraft taxied toward the runway. During taxi, the pilot and two pilot-rated passengers discussed that a thrust reverser indicator light for an unspecified engine was inoperative, though they believed the thrust reverser itself was working properly. Meanwhile, the right-seat passenger attempted to contact ZTL ATC and activate the flight’s IFR flight plan three times between 10:08 and 10:10 but was unsuccessful due to the controller’s workload and associated...