You have two problems: something is open in the heater circuit, probably the thermal cut-off because the dryer got clogged with dirt and no one took it apart and cleaned it; and, you most likely have a bad timer where a set of contacts that sends power to motor are welded together.
You are going to have to take it apart to clean it and find the thermal cut-off and test it with a meter and you will have to test the timer contacts. You will need a multimeter to track down these problems. Here is a book to help: http://dl.dropbox.com/u/8010163/Whirlpool%208178584%20Cabrio%20Dryer%20Service%20M anual.pdf
and: http://dl.dropbox.com/u/8010163/Whirlpool%20ML-4%20Maytag%20Centennial%20Dryer%20Service%20Manual .pdf
and: http://dl.dropbox.com/u/8010163/Kenmore%20Dryer%20Manuals.zip
I hope these help. When you remove the rear cover of the control panel where the timer is located you will see a tech sheet. If you will scan this to a jpg file and send it to
[email protected] I will see what I can do to help you. The manuals I posted for download should be close to yours as they are all pretty much the same except for minor differences.
Sent legend via regular email. Will be looking at dryer on Friday. Hope this legend helps.