Starting issues (2009 Mazda6)…Any ideas?

Test drove a 2009 Mazda 6 Touring for my sons first car- ran great. Got it home and two weeks later discovered that the alarm would go off randomly. Unhooked the battery (to get some sleep) and when I hooked it back up, it wouldn’t start. Tried troubleshooting- changied fuses, relays, battery in key fobs, tested year old battery and its good. Needed to move the car so I put it into neutral and got it out of my driveway. Hooked battery up again and it started. I didn’t drive it. A day or two days later I dove it to work - parked it on a slight incline and when I left work it wouldn’t start. Can’t even get it into neutral. Looking for ideas. No Mazda dealership nearby.
 
Back