You should be in SA mod anytime the slide is pulled back, regardless of a shell in the chamber or not. DA mod should only happen after the trigger is pulled on an empty chamber or dud round. So assuming you can't get into SA mod reliably, there is most likely a problem with the firing pin assembly assuming that the trigger is functioning properly. Are you comfortable with disassembling the firing pin assembly in the slide? If not you can atleast check it for movement by removing the slide and manually operating it with your hand. See if it is free, sticky or other signs of wear/malfunction. If there is you can attempt to fix it, clean it or send it in for repair.
This is a common area in nearly all firearms for this type of malfunction. Let us know what happens.