Besides the possibility of a clogged vent that is preventing air movement through the dryer, and a burnt out dryer heating element, you should also check the thermostats.
Dryers will typically have two thermostats; a low temperature thermostat that is used when the dryer is set on the "Delicates" cycle and a high temperature thermostat that is used on both the Regular and Permanent Press cycles. (The difference between the Regular cycle and Permanent Press is that on the Permanent Press cycle, the heating element will typically shut off 5 to 10 minutes before the end of the cycle so that the clothes continue to tumble as they cool down. That prevents creasing of the clothes which would otherwise have to be ironed out.)
So, if your dryer doesn't work when set on the Regular cycle, you can check to see if the problem is a burned out high temperature thermostat by running the dryer on the Delicates cycle. If the dryer seems to work then, the problem is the high temperature thermostat is busted.
If the heating element shows continuity, but the dryer doesn't heat on either cycle, you can also check the auxillary switch on the dryer motor. The purpose of this switch is to prevent the heating element from coming on until the motor comes up to full speed. This is because both an electric motor that's just starting and the dryer heating element with both draw a lot of current, which would otherwise cause the dryer to blow fuses or trip breakers. The auxilliary switch on the motor prevents current flow through the heating element during the first one or two seconds while the electric motor is coming up to speed. Once the motor reaches it's normal operating speed, then power is applied to the heating element.
It's possible that the auxilliary switch on your motor is busted, and not allowing power to flow to the heating element even after the motor reaches normal operating speed.