A common problem on older model Whirlpool and Kenmore dryers. Let's face it.. years of use and sometimes "Abuse" dryer motors are going to fail. A common warning sign for a failing motor is a loud start up.. you press the start button and you hear that bogging down sound, grumble noise, sometimes you can even notice the lights in the laundry room dim. Sometimes you press the start button and and just hear a loud buzz, then nothing.. all signs of a failing dryer motor or a motor that has failed.
The most common Whirlpool & Kenmore dryer motors for dryers made in the late 1990's up through 2010 is this motor part#279827 https://www.thriftyapplianceparts.com/279827-whirlpool-dryer-drive-motor-replacement/
Another common motor for these dryers is this one part#279787 https://www.thriftyapplianceparts.com/279787-whirlpool-dryer-drive-motor-replacement/
Please check with Thrifty Appliance Parts
to make sure which one is for your model. It is not a simple repair job changing out a motor but with all the useful videos out there and places like Thrifty Appliance Parts offering a Non-OEM alternative part you can literally save yourself hundreds of dollars!