Here are your parts
Replacement parts for FEX831C models | AppliancePartsPros.com

Here is the wiring diagram
http://manuals.frigidaire.com/prodinfo_pdf/Webster/1341356aelec_sheet_1.pdf

There is a problem with your testing procedure.
The air is ambient sucked over the heating coil, through the drum and then pushed out the exhaust by the blower. So if you run it with the door open no air is going over the coils, it will overheat and open the hi-limit thermostat. It will then take a long time to reset due to no air flow to cool it down.

The most common cause of long dry times is a dirty/malfunctioning vent system.
Undo the dryer from the exhaust
Run a load
If the load dries correctly then you have a vent problem.
Clean/check the vent system. Make sure the outside louvers open fully.

If you do not want lint in the house.
Take a pair of pantyhose, put one leg into the other and attach this to the dryer exhaust.
Leave enough room behind the dryer so it can blow out like a windsock.
Run a load.

Both the above will allow you to check the air flow and temp.

Also check that the blower wheel is clean and solidly attached to the motor.

Another possibility would be a grounded element.
Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run but only part of the element heats up.

Next I would check the fabric selector switch to be sure it opens when you select high heat.