Dinosaur boards are the way to go on a replacement. While there are several other things that could be wrong, the lack of even a click would lead you in the direction of the board. A faulty sail switch might also keep the gas valve closed and the ignitor off but typically will leave the fan running instead of shutting down the entire unit. The time delay unit could also be a potential problem. You can wire around it to be sure it is working properly.
The only one I have bought I got from an RV repairman but you might check with
http://www.marksrv.com/suburbanparts.htm.