Tim Aikio, First of all, if the phone has been left to discharge for a month, it’s perfectly normal for the phone to initially show the low battery symbol. It will be there until it’s charged enough to boot up. Just leave it charging, and you should be a step further.
Second, the method you’re describing is not entering diagnostic mode, it’s a hard reset.
To enter diagnostic mode, press and hold both volume up and volume down. While still holding the buttons, connect the phone to a charger or computer, then release the buttons when the Apple logo appears.
Note! The phone (battery) need to have enough charge to boot in order to enter diagnostics.