How can I get my Sears Kenmore clothes dryer to start?

This 12 year old dryer will not turn on. There was no "warning": an hour ago, it worked fine; now it will not start. Before I took anything apart, I noticed that, when I pushed the start switch, I could hear some sort of slight mechanical "click" in the timer but the dryer would not start. I took out the push-to-start switch (part # 279173) and can see evidence of damage (burnt contact) inside the clear plastic housing. Becasue (inspite of the burnt contact), the push-to-start switch DOES appear to still make electrical contact, I am wondering whether or not the timer (part #3398194) may (also) be bad. Should I replace one or the other or neither or both? At Sears the swith costs $37.59 and the timer goes for $80.27. Can these parts be found for less somewhere other than Sears? [For about three times the cost of these two (minor) spare parts I can buy a NEW dryer!!]