Check the following to address this issue.
1. No power to the dryer
Make sure there's power getting to the dryer. Check for a
tripped circuit breaker or a blown fuse. Check the wall socket for
power with a voltmeter or by plugging something else in.
2. Door switch / Door switch actuator lever
The dryer would not start with a broken door switch. Replace the
door switch if found defective.
Most dryers have a door switch actuator lever - when you close a
dryer door, it presses against the lever, which actuates the door
switch. If the lever is broken, the switch would not activate and
the dryer would not start. Replace the lever, if broken.
Note: Door switch actuator lever usually comes with the door switch
assembly and it is recommended to get the whole assembly since there
is almost no price difference between the door switch assembly and
just the lever. Check your model for more details.
3. Thermal fuse
Most dryers have a thermal fuse, which burns out when the dryer
overheats, in which case the dryer will either not run at all or
stop heating. The fuse is usually located on the vent duct, inside the
dryer. A blown fuse will show no continuity when measured with a
meter. Before replacing the fuse, make sure the blower wheel is not
broken or clogged, and there is nothing blocking the venting.
Note: It is recommended by most dryer manufacturers to replace a
hi-limit thermostat when replacing a thermal fuse.
Replace if defective (note: uncommon problem).