Your mistake is that you tried to use instructions for the electric dryer while having problems with the gas dryer. The troubleshooting is different for those dryers.
The fist thing you may want to check for continuity is the thermal fuse (#6 on the
diagram). If this fuse is open, replace the cycling thermostat as well and clean the dryer vent line.
Quote:
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...In the AppliancePartsPros.com website, its listed simply as Thermostat (part no. AP3134945) and it fits together with the cycling thermostat (AP3115922)...
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This part is actually a heater. The normal resistance reading should be between 5000 Ohms and 9000 Ohms. If the reading is incorrect, replace it too.
There are two different thermal fuses listed for this dryer by Whirlpool (weird), so you have to determine which one is used in your dryer before order any.
- The thermal fuse
Part number: AP3132867 
- The thermal fuse
Part number: AP3133489 
- The cycling thermostat
Part number: AP3115922 
- The thermostat heater
Part number: AP3134945 
Here are the breakdown diagrams and
Replacement parts for WHIRLPOOL LG5796XPW0 Residential Dryer | AppliancePartsPros.com
Gene.
P.S. You can find some useful information in one of our previous threads:
No Heat on Gas Dryer