How to reprogram car key fob for keyless entry remote for mazda3 2011 S

When I got the car I had 2 fobs, one I use every day and a spare. (The spare never worked though as keyless entry).
I lost the original fob and I’m left with the spare one that doesn’t open/start the car keylessly but I use the physical key inside of it insert it manually into the door and the ignition. I made a physical copy of the key and this new copy open the external door but doesn’t start the car when I insert it in the ignition. I also tried to reprogram the fob following some instructions I found online but didn’t work. I need the car to open electronically and possibly to start as it was originally made for. Is there a way I can reprogram the keyless entry with basically just the physical key inside have (part of the fob that doesn’t work) without paying $500 for that- or if not, would it be possible to have the doors opened by a different fob or system so I can access the car quickly and then keep using the original key I ve got- I’m willing to try anything possible as I work with the car and go in and out of it hundreds of times per day and cannot pay the $500 and up everyone is asking for a fob. I would love to understand what possibilities there areif any as the info online are not forthcoming nor cohesive - thank you so much! Diana