That piece has been recalled just take it into your Mazda dealership and they will replace the recalled piece. I had the same issue
What kind of auto is it. Sounds like you may have an ignition switch problem.
Sounds like exhaust leak.
Sounds like the engine heats and the ignition fails.
Sounds like alternator is going bad even though it still may still hold a charge
Your Accord is overheating. The fan is running to try and cool the engine off. seek professional help immediately before you destroy the engine.
Are you just trying to start the engine, or is it already running? If it is running it sounds like the power steering pump is bad.
Sounds like one or more rods in the engine broke.
Sounds like a dead battery. You need the battery to start the car, but once it is running the engine runs completely off of the alternator (which also recharges the battery if the battery is still good).
Sounds like you have a faulty thermostat. Its nothing expensive on hard to replace.
It sounds more like you are hitting the starter again after the engine is running.
Sounds like the fuel pump is running May be a failed relay
It sounds like your dizzy cap isn't lined right which causes the engine to stay running after the ignition has been switched off. i had the same problem with my fiesta