Here are your parts
Replacement parts for WHIRLPOOL REX6634RQ0 29" Electric Dryer | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%208528187.pdf

First try flipping the breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker and the heating coil requires the full 240 volts.
If this does nothing.
Get a meter, see below.
Measure the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the unit's terminal strip to ensure they are properly connected and none of them have burned off
If OK
Plug the unit in and check the voltage at the terminal strip. This is just in case you have a bad line cord.
[COLOR="Red"]Be careful 240 volts is lethal.[/COLOR]

If OK
Unplug the unit and check the heating coil and thermostats etc. for continuity.
Heating coil, should be 10 ohms approximately.
Thermostats and thermal fuse all should be 0 ohms.
If the thermal fuse on the heater is blown then there are other things to check before replacing it.


If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.