If the battery is dead how can they turn it on to find out what the problem is? Literally an unsolvable problem.
Takes 5 seconds to probe the battery with a multimeter and see its dead. Those are basic troubleshooting steps that some 10 year olds can do, let alone a professional repair shop.
And any device built to be serviceable has diagnostic probing points on the pcb for stuff like this, even iPhones
Given the absolutely clueless troubleshooting you suggested in the 2nd paragraph that was not exactly clear