This model uses an engine immobilizer as part of the anti-theft. You could leave the wrong key in the ignition for days, with no success. The key has an electronic resistor built into it that the car's ignition will read. Even if the key is cut correctly, if the chip inside doesn't transmit the right signal, the car will not, under any condition, start............
GM's PASS-KEY System, such as those used on a Chevrolet, allows for any key that was cut to fit the ignition, but did not transmit the right code, to start the car after 17 minutes delay. The idea was that a thief would not want to wait around very long. Your mom's Mazda is more demanding, and therefore, more secure. Please review section 3, pages 20 through 22 of the owners manual. I've posted the link to a digital copy of it below this message. Do consult with your selling dealer, because this rarely happens on next-to-new cars. They should replace her keys and reprogram the immobilizer for free. It should definitely be covered under warranty, especially since she's only driven it such few times.
Hope this Helps!
Owners Manual Linkhttp://www.mazdausa.com/MusaWeb/pdf/manuals/2008_Mazda5_OM.pdf