The furnace will turn on and run for approximately 5-10 minutes. Upon igniting, the blower will soon kick on. After the said 5-10 minutes, the blower will kick off and the damper door will remain on with no flame and will not reset by itself. I manually have to turn it on and off. I would greatly appreciate any insight as to what the issue may be, as I have come to a few conclusions myself but I do not have experience working on furnaces.
Thanks for any help.

It sound like a limit is opening. The trick is witch one. Your furnace should give a fault code when it malfucntions. Count the blinking light on the control board of the furnace. The code should be on the front or back of the blower door.