Kenmore 70 Series Dryer

The dryer starts and runs. It does not heat or time out.

Here is your wiring diagram, see the attachment.

If the timer does not advance in both auto and timed dry modes, odds are you have a power problem.
In timed dry the timer mpotor runs directly off the 240 volts through Timer Switch 0 WB/TM contacts. The heater also runs off of the 240 so if both are not working the first thing to check is the power,

Try flipping the breaker off/on slowly a couple times, sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
Be careful as 240 volts is lethal !!!

If it does advance in timed dry then the first thing to check would be the heating coil.
Should be about 10 to 12 ohms.