I have a Kenmore dryer also and had the same problem that was already mentioned with the Relay. However, I didn't get it from Sears I got it from the manufacturer and only paid $5 for it (the part number for the relay is on it as well as the manufacturer)... anyway, my point is that you can check the relays with a meter and check the resistance between the two contacts to see if they are in range. You can usually get the part from jameco.com .
Sounds like that is the issue. Also, do you have thermo resistor (or something) that goes into the exhaust or near the elements to make sure it doesn't overheat? I wouldn't think that would be the issue, since usually if that goes it still spins, but doesn't produce heat. The other issue I had with my Kenmore dryer was the "Even-heat" logic board, but I didn't see anything like that on your dryer.
If you don't have a meter, you can try swapping the two relays (one is for heat, one to spin) and see if you can get the dryer to spin without heat. If you can, then it is a bad relay. If it still doesn't work, then you are no better off.
Sounds like that is the issue. Also, do you have thermo resistor (or something) that goes into the exhaust or near the elements to make sure it doesn't overheat? I wouldn't think that would be the issue, since usually if that goes it still spins, but doesn't produce heat. The other issue I had with my Kenmore dryer was the "Even-heat" logic board, but I didn't see anything like that on your dryer.
If you don't have a meter, you can try swapping the two relays (one is for heat, one to spin) and see if you can get the dryer to spin without heat. If you can, then it is a bad relay. If it still doesn't work, then you are no better off.