Here are your parts
Replacement parts for GE DWSR473EV1WW | AppliancePartsPros.comFirst let me say getting info on GE's is a pain they like to keep all tech info a secret. Take a look in the control console to see if you can find the wiring diagram for your unit.
Here is a link with some sample wiring diagrams
http://www.applianceaid.com/dryers.html Click on 5 GE, then 28 Sample wiring, then 4 or 5. 4 being the simpler.
I looked through the parts but could not find a moisture sensor so this is probably how it works:
On timed dry the timer motor gets power directly from the line Neutral to L1, 120 volts.
On Auto it gets power when a heater shuts off, 240 volts and a resistor (Item 80 in Section 1) reduces it to 120 volts for the timer motor.
Your unit has 2 heating elements. It could be that one of them is burned out. Then depending on what temp you are running the other element never shuts off so the timer never advances. Also it could be that an element is grounded in such a way that it never shuts off.
Unplug the unit.
Remove the wires from the heaters, mark where they go.
Measure them with a meter, each should be about 20 ohms.
Then measure each connector to the case, all should be infinite ohms (open)
Another possibility would be the resistor is blown. Unplug the unit, remove one wire from it and measure it. Not sure what it will be as it depends on the model but usually around 4,000 to 5,000 ohms.
There are other possible causes but the above are the most common.
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. Also it lets you check most things with the unit unplugged which is much safer.
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.
Hope the above is useful to you!!!