If the door switch is faulty it won't start, the dryer thinks the door is open.

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Parts for Roper RED4000SW0 Dryer - AppliancePartsPros.com

See the attachment for the tech sheet.

You checked for the 240 at the outlet but did you check for 120.
I would check this at the terminal strip in the unit.
It is the L1 no Neutral side that is the motor power.
[COLOR="Red"]Be very very careful as there is 240 at the terminal strip and that is lethal!!![/COLOR]

[COLOR="Blue"]And continuity on the thermal fuse, the push to start button, the timer, the heating element and the other fuse that's there. [/COLOR]
The heating element and irt's control thermostats should not effect the motor starting.

[COLOR="Blue"]The only thing i didn't check was the motor; because nothing is turning i figured the motor wouldn't cause it.[/COLOR]
No, a blown motor will cause the unit to not start.

So lets check the motor circuit.
Set your meter to it's most sensitive resistance scale.
It is a good idea to short the meter leads together before starting so you can see if the meter has a zero offset.
Set the units timer to mid scale heated dry.

Unplug the unit and tape/clip one meter lead to the L1 prong on the line cord and leave it there.
Now work your way back through the circuit.
L1 (black) on the terminal strip should be 0 ohms.
BK and BU at the timer should be 0 ohms.
Both sides of the thermal fuse (on the blower) should be 0 ohms
4M at the motor should be 0 ohms
5 M at the motor should be about 1.5 ohms (motor windings).
With the push to start switch pushed both sides should be 1.5 ohms.
Keep it activated
Both sides (common to normally open) of the door switch should be 1.5 ohms with the switch/door closed.
Keep it closed
Neutral (white) at the terminal strip should be 1.5 ohms
The Neutral prong on the line cord should be about 1.5 ohms.

That is the entire motor cicuit.