The dryer won't turn

Can you hear the motor start? If so, for many Kenmore dryers you will need to remove the top and front of the dryer to install a new belt. You will have to support the drum. Make sure to check the belt tensioner. Unless you have some basic tools and are reasonably good taking things apart, let a service tech do it.

Make sure to clean it well and lubricate it with lithium grease or it will fail very fast. DrTom4444

How to take off front of Kenmore soft heat heavy duty dryer

It sounds like you have a broken belt, but if has run long enough to wear out the belt it needs cleaning, too. You need to totally tear it down and scrape out and wash all of the parts except the motor, which you vacuum out. You can go to YouTube to see videos on how to take it apart, but do a very good job or it will fail again quickly. . I would get a new belt and change it while you have it apart and get some white lithium grease and grease any bearings you find. You need to clean out a drier every two years, at least, according to the manuals.
Look at: How to clean your clothes dryer. How to make it hot again. - YouTube (http://www.youtube.com/watch?v=MMP7BW1lLs4) to see how to tear it down. Also: Mr. Appliance Tips: How to Clean Your Dryer - YouTube (http://www.youtube.com/watch?v=iBiRw-KElC4) ; Cleaning a Dryer Vent and Lint Trap - YouTube (http://www.youtube.com/watch?v=yFTZGgVisCI)
Electric Clothes Dryers (http://www.electrical-forensics.com/Dryer/ElectricClothesDryers.html)
Whirlpool Dryer Model LE5800XSW3 Wiring Diagram | Dryer Repair | Fixitnow.com Samurai Appliance Repair Man (http://fixitnow.com/wp/2010/10/09/whirlpool-dryer-model-le5800xsw3-wiring-diagram/)
The job is very easy for a woman to do. Just get it out into your garage or somewhere you will have plenty of space. Pop the top and unplug the wiring harness, then you can see where the screws are that hold on the front. You will need to unplug the door switch. You should lay it on its back to make it easier to work on before pulling off front. Make sure to clean it very well and don't miss the duct on the door going to filter or the other ducts in the rear, and the blower wheel which is very, very important. A clog of cement-like lint build up can hide anywhere. Don't be afraid to take apart anything to be able to look inside and clean it. One missed place will necessitate doing all this again and no one wants to redo something. Grease all support rollers
With white lithium grease and reassemble and you have a new dryer.