The click that you hear is likely the relay in the control board closing to supply voltage to the drive motor circuit. This dryer has a broken belt switch. The motor will not run if the drive belt is broken. I recommend checking for this failure first. To check the belt, you can
unplug the dryer
and remove the top panel. Screws at the back edge of the top panel secure it to the dryer frame. Remove these screws and pull the top panel back slightly and then up and off of the dryer. If you find that the belt is broken, you can order a new one from the Sears PartsDirect website
. The part number is 661570.
If the drive belt is okay, then you could have a blown thermal fuse that is preventing the dryer motor from running. The thermal fuse is shown in the first image below. Be sure to
unplug the dryer
before accessing this fuse. The second image below shows the procedure for removing the lower front service toe panel. Remove this panel and locate the thermal fuse on your dryer.
NOTE: Internal metal edges in the dryer can be sharp. Protective gloves are recommended.
Remove at least one wire from the thermal fuse (light blue wires) and measure the resistance across the leads of the fuse using a volt/ohm meter. You should measure near zero ohms of resistance (continuity). If you measure infinite resistance (open), then the thermal fuse is blown and will need to be replaced. The part number for the thermal fuse is 3392519.
If the thermal fuse and the belt are both okay, then you could have a failed drive motor or problem with the broken belt switch. A wiring problem could also cause this problem.
If you need more help with this repair, resubmit your question with additional details.