The blower starting triggers all of the other functions of the furnace. Most furnace control boards have an LED on it that will flash blink codes to help you troubleshoot. If it is not lit up, there's no power to the furnace or the control board isn't working.
I had my furnace fill up with water due to an improperly mounted exhaust port, and the blower still worked, it just wouldn't stay lit. Definitely make sure power is going where it is supposed to go. I hate to say this, but if you find power at the terminal block and you can't get at the control board, you are going to have to pull the furnace out to troubleshoot it. Fortunately it is easier than it looks once you find all the mounting screws.