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The thermistor (part(###) ###-#### ***** read no continuity because the resistance is incredibly high on this part. It's roughly 10,000 ohms at room temperature. Either way, if the dryer isn't giving you and error code and refusing to start, then the thermistor isn't your problem. The element you said was good so we'll assume it's good. There are 2 more devices mounted to the left side of the heating canister. You'll need to test continuity through both of these devices and if either part doesn't have continuity, replace it.
Other than that, make sure the dryer is getting 220 volts between the 2 outside power wires on your power cord right where it connects to the terminal block on the back of your dryer. If the dryer is only getting 110 volts, the dryer will run but it will not heat.
As a last resort if the dryer is getting 220 volts and the heating element and both devices mounted to the left side of the heating canister have continuity---your main power relay board mounted to the left side wall of the dryer under the top panel has failed and would need to be replaced because it's not sending power out to the heating element like it should.
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