If it indeed started that one time for a short period then cut out, the first place that I would start would be the capacitor located in the blower compartment. The capacitor gives the motor the need kick to start, and often times stays in the circuit to help the motor run more effeciently. This could very well be the problem.
If you have the option to run the fan from the thermostat, turn the fan to the "on" position and see if it starts. If it does, then it is not the capacitor.
Hope this helps
PS Your are correct about the "sensor" turning the furnace off, it is called a high limit switch and is there for safety. It is an automatic reset device, and will reconnect power once it has cool suffeciently.
Testimonial: "Thank you so much for this help. We discovered a wire had worn through from the vibration of the motor, replaced the wire and good to go. Phewwww! "
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Never mind, we troubleshot it and it's a wire from the motor that has worn through against a piece of metal with vibration from the motor. ahhhh, thankfully nothing $$$$$.
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