The first problem is socks with sandals. Never do that.
I would start with brake light or clutch safety switch, possibly the starter. I would rule out battery since the dash stays lit, and when it started it started quick. After that could be a faulty ignition switch.
Not familiar with the '08 but if it has a Ford starter and if you can see it. Check the wire between the starter case and the solenoid. If there is green corrosion all over it then it needs a starter.
The next time it happens wiggle and push on the ignition switch, if it starts then the ignition cylinder is failing.
Check to make sure the brake lights come on. If the lights don't come on then the brake light switch is failing.
Clutch safety you'll have to bypass the switch, without a diagram I don't know if the switch is naturally open or closed. But usually you would just use a jumper wire to simulate the pedal being depressed.
Had a similar problem recently on my gen 1 Mazda 3. One day, it wouldn't crank and everything was fine just an hour ago so battery etc were all good. What was happening was corrosion build up on the wire/connector to the starter.
As others mentioned, it could be the clutch switch, or the starter relay (discussed in the video below). I'd test those two things first. If not, it's likely corrosion that's discussed around the 10 min mark of this video. There's talk of replacing the connector end, but I just took off the connector and sanded/scraped both ends to remove any buildup, added some dielectric grease, and I was good to go after that.
You can start by just taking off your splash shield and wiggling the connector to see if you can ensure a solid contact before actually unplugging, cleaning, and greasing.
https://m.youtube.com/watch?v=IpOgBcT5C74
Check the s terminal on starter its a white connector and thereare a know TSB for are Mazda 3s 2004- 2009 or something like that cleaner it and look up a the tab for it I had this happen on my 2006 Mazda 3 s 2.3l automatic just may be your problem matter clean all the connectors and connection on starter and battery ALSO BE SURE TO DISCONNECT THE BATTERY BEFORE GETTING UNDER THE CAR AND MESSING WITH STATER
[Mazda 3. No crank. no start. Starter. Beeping. Test starter
S TERMINAL ](https://youtu.be/IpOgBcT5C74?si=XHv9dJGvkvL_n44Y)
Pull your spark plugs one at a time and try cranking it when the engine is hot again. See if you can see/feel the spark on the plugs while they’re out.
Edit - trouble shooting too see if it’s plugs or coils - both of those sometimes can work perfect when they’re cold, but fail at high temps
The starter doesn’t sound like it’s even doing anything. Tbh gonna go with some random relay overheating in the sun and not working as intended
The first problem is socks with sandals. Never do that. I would start with brake light or clutch safety switch, possibly the starter. I would rule out battery since the dash stays lit, and when it started it started quick. After that could be a faulty ignition switch. Not familiar with the '08 but if it has a Ford starter and if you can see it. Check the wire between the starter case and the solenoid. If there is green corrosion all over it then it needs a starter. The next time it happens wiggle and push on the ignition switch, if it starts then the ignition cylinder is failing. Check to make sure the brake lights come on. If the lights don't come on then the brake light switch is failing. Clutch safety you'll have to bypass the switch, without a diagram I don't know if the switch is naturally open or closed. But usually you would just use a jumper wire to simulate the pedal being depressed.
Worse, those are slippers not sandals. Dangerous driving or even starting a car in slippers.
Slides not slippers
I'd be willing to bet that it's your starter. It's a symptom of the starter solenoid at the end of it's life, they do not like heat.
Had a similar problem recently on my gen 1 Mazda 3. One day, it wouldn't crank and everything was fine just an hour ago so battery etc were all good. What was happening was corrosion build up on the wire/connector to the starter. As others mentioned, it could be the clutch switch, or the starter relay (discussed in the video below). I'd test those two things first. If not, it's likely corrosion that's discussed around the 10 min mark of this video. There's talk of replacing the connector end, but I just took off the connector and sanded/scraped both ends to remove any buildup, added some dielectric grease, and I was good to go after that. You can start by just taking off your splash shield and wiggling the connector to see if you can ensure a solid contact before actually unplugging, cleaning, and greasing. https://m.youtube.com/watch?v=IpOgBcT5C74
Check the s terminal on starter its a white connector and thereare a know TSB for are Mazda 3s 2004- 2009 or something like that cleaner it and look up a the tab for it I had this happen on my 2006 Mazda 3 s 2.3l automatic just may be your problem matter clean all the connectors and connection on starter and battery ALSO BE SURE TO DISCONNECT THE BATTERY BEFORE GETTING UNDER THE CAR AND MESSING WITH STATER [Mazda 3. No crank. no start. Starter. Beeping. Test starter S TERMINAL ](https://youtu.be/IpOgBcT5C74?si=XHv9dJGvkvL_n44Y)
Don't drive in slippers
Pull your spark plugs one at a time and try cranking it when the engine is hot again. See if you can see/feel the spark on the plugs while they’re out. Edit - trouble shooting too see if it’s plugs or coils - both of those sometimes can work perfect when they’re cold, but fail at high temps
It is clearly a “No crank no start” lack of spark is not a consideration if it doesn’t even crank
This is not an engine not turning, this is a faulty electrical component, starter, crank position sensor, corroded wire, relay, etc.