A flapper-door in the exhaust hood is to prevent small animals from crawling in and block outside air from blowing in. It should of course open via the airflow force when the machine runs, close via gravity when the dryer is off. It has no relation to the dryer not heating, that is a problem with the dryer. Choice of several possible causes ... thermostat, thermal fuse, timer or control board, heating element or gas burner, centrifugal switch on the motor, electric supply / breaker problem if 240v electric model. You didn't reference a model number.

Thank You! It's a Kenmore Oasis and pretty old, I will troubleshoot your suggestions and truly appreciate your time!

Oasis is a marketing name. The model number tag on the machine is much more specific, should be somewhere around the loading port visible when the door is open. The serial number is coded for the year and week of manufacture. Cite it here if you want to know the age more precisely. Dryers are simple machines (gas is a bit more complex with the burner components), typically valid to repair if not physically cratered from abuse or a needed part hasn't gone unavailable. I refurbed some common mechanical wear-parts (belt & rollers) on my neighbor's 20yo dryer last June for $73 parts cost, it oughta run another 10 to 20 years.

If you have a flapper style vent, the flapper and or flapper hinge could be caked up w/ accumulated lint. When was the venting last cleaned out?