Wow, this is unusual. Does it spontaneously start when the timer is in the off position?

First, let's confirm or eliminate the start switch as the problem.

Unplug the dryer, then take off the console and tape the two wires that connect to the start switch together. Then plug in the dryer. If it starts, then you will need to replace the start switch. (do not operate the dryer in this manner!) If not, post and let's see if we can come up with something else.

Good luck.