Providing the replaced battery and alternator are in good working order and your car is not starting because of a low charge on the battery, you most likely have an electrical draw on the battery from somewhere in the system. The attending technician would have a meter hooked up to the system and would, one by one, disconnect the individual circuits and notice when the draw stops on the meter. Then the technician would isolate the offending item within that circuit, most likely using a wiring schematic.
Excuse the possible poor question but -- have you verified the battery is capable of accepting a charge? If you have not had it professionally tested, do so to make sure it is good, regardless of the age.