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If the draft fan doesn't run nothing else will happen. You need to check to see if the fan is getting voltage. Probe the leads to the fan. If it is getting power and it's not running then a new fan would be in order. You should jump the R & W terminals at th furnace terminal strip if you're not sure the thermostat is calling in the furnace.
If you have a call for heat you should have voltage to the fan. If you don't then the board is suspect. A bad connection is always a possibility but if you probed at the board then that should rule out a connection issue
You can try hot wiring the fan but if you don't have voltage from the board it's unlikely the fan is faulty as well. You'll have to improvise the line voltage connection to the fan if you still want to try this.