I think the dryer cycling t-stat may be bad. I have voltage at the top and bottom of the swith, but not on the sides ( violet wires). Would jumping these wires make the dryer heat? Everything else seems to checkout. I did notice that I only have 120v across the element. Would this t-stat have an effect on that?

Here are your parts
Replacement parts for WHIRLPOOL REX4634KQ0 | AppliancePartsPros.com

Here is your wiring diagram
http://www.servicematters.com/d...0Sheet%20-%203406688.pdf

I think the dryer cycling t-stat may be bad. I have voltage at the top and bottom of the swith, but not on the sides ( violet wires). Would jumping these wires make the dryer heat?
Do not jump these wires they are the internal heater and you will put a dead short across 120 volts.
If you have 240 volts across the operating thermostat's contacts at room temperature then it is bad. It should be 0 volts.

I did notice that I only have 120v across the element. Would this t-stat have an effect on that?
If you have a true 120 volts across the heating element it should be heating up, though at half the watts of it's normal operation.

PS: Just a thought, why your are testing with the unit plugged in and risking a shock, burn or worse when the heating circuit can usually be checked with the unit unplugged using resistance.