how can you tell if it is a battery, starter, or alternator problem?

if its an alternator problem, there will be no charge, look for charge warning light and if its working you should get 14 volts across the battery terminal, if its the starter you may here a whine or a click meaning either the starter or the starter solenoid not working, if its the battery you may get no warnings light gauges etc and a click when operating the starter, if you have none of them symptoms then check all connections to and from the battery, remove clean and re-fit. my advice to you is to find a specialist qualified technician to diagnose your automobiles malfunctioning electronics

Have the battery load tested. Check the alternator output with engine running at the battery terminals 13.5 -14.8volts Ok

Go a PAT volts car not running and volts are at 13.3is this still ok