Electric dryer stopped running

at first it would run awhile, then stop by itself without being finished with time cycle. now it will not start up at all, even when cool. cleaned out the vent and the lint area, the light inside the dryer is on when door is open so it's getting power. The gradual stopping of working is confusing. It would only run for maybe ten min and then it would cut itself off before. I thought overheating so we cleaned out the lint areas. After cleaning those out, it won't come on at all. HELP. The dryer is a kenmore from sears. 500 series if that means anything.