Product review (5 stars): Very easy repair
Our 23 year old Kenmore gas dryer stopped working three days ago.  The dryer was made by Whirlpool.

Unplug the dryer first before testing the components...

I checked the fuse in the back after removing the back panel.  That was fine.  I pulled off the dryer bottom panel and removed the one screw holding the Flame Sensor.  I removed the Flame Sensor and tested the continuity with a multimeter.  No reading.  That indicated the Flame Sensor was shot as it should show a reading when cold.

You can test the dryer while the Flame Sensor is removed.  First separate the two flame sensor wires a few inches.  Plug the dryer back in and close the door.  If you press the start button, nothing will happen with the removed Flame Sensor.  Touch the two wires that go to the flame sensor together.  The ignitor will glow red hot within seconds.  When it is red, remove the wires a few inches from each other.  The gas will turn on and the dryer will heat like it works.  DON'T RUN THE DRYER LIKE THIS.  It's not safe to have two exposed wires in an appliance that vibrates.  This is just to check it to see if it the ignitor is ok. the gas turns on and ignites in the burner tube.  Basically we are confirming all the other parts are aok.  Shut the dryer off and unplug it until you replace the flame sensor.

I got this part in two days with Amazon prime and it took 5 minutes to replace.  My dryer is good as new for $15.

Fix old gas dryers...don't get rid of them because you are dazzled by electronic read outs or anti-wrinkle features.  The new dryers with more elaborate electronics/circuit boards all fail in 1/2 the time.  My Jenn-aire range that is 15 years old I have replaced the clock 2x and the main circuit board/controller due to leaking capacitors, etc.  Old gas dryers are simple and built to last.  A time dial, start button, and a buzzer when it's done.  Not many parts to break down!

UPDATE: February 2016-  Our gas dryer is now over 25 years old and has worked perfectly since I replaced the Flame Sensor.