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Check the door switch for both voltage and ohms. Your description of the problem leads there.
Please let me know if you have any other questions.
Also, the relay on the motor (which acts as a switch) should be checked.
This site will help explain more -
ok, the door switch will not let the time advance....
please check the two items and let me know what you find .....
Do this - - set dryer on a no heat setting , put timer on a timed cycle ( not any automatic cycle ) I want you to check the voltage at the timer On the timer is a round motor with two wires that connect to the body of the timer , you should have 120 volts on these wires > If you do the new timer is defective. If not, make sure you haven't mixed up a wire when you replaced it.