The dryer was having trouble starting, and it would try to begin turning, and then "click!" it would trip its internal breaker. I looked through the list of possible causes, and ordered a new set of rollers since that was the least expensive starting point. I decided to change the belt too since the old one looked pretty worn out.
Changing the rollers and belt was very easy, especially with the helpful video. After completing the repair, the dryer turned on... and then promptly shut off with a "click!" Well, on to the more expensive fixes.
Next in line was changing out the drum motor. I ordered the motor, watched the video, and when the part arrived I was totally prepared. The motor swap took about 30-45 minutes, and now the dryer works perfectly again.