When you set the timer to the timed dry cycle, does the timer advance normally while the drum is tumbling? If not, try resetting the AC panel breaker for the dryer. Sometimes, one half of the double pole breaker can trip without tripping the whole thing. If that doesn't fix it, then you need to use a multimeter to make sure you have 240vac at the dryer power cord connection block on the back of the machine. If 240vac is good and the power cord connections are intact, then I would replace the timer. The type of timer used on this dryer is a real piece of junk and they fail often. The other remote possibility is a faulty motor centrifugal switch which would require replacement of the motor.

Whirlpool W10185988 Timer - AppliancePartsPros.com

Eric