Find your starter (usually on the bottom of the engine), and give it a good thawck with a hammer. If it starts after that, it's an issue with the starter. Some this else to check is that the spark plugs have spark and are properly gapped.
This sounds like it could be a bad thermal fuse. You'll want to check both fuses for resistance with a multimeter. If either one reads more than 0 ohms, it's faulty. Make sure to clean out the lint from the back of the dryer, since that's what will usually cause those to fail.