I don't know about your furnace, but some have a safety switch on the door or cover panel that will keep the furnace from coming on if the panel isn't installed properly. But, if I remember correctly, that would also keep the blower from coming on in the A/C mode too. If the outside A/C unit comes on and the inside blower comes on, in the A/C mode then you can pretty well eliminate 110v and transformer problems. Seems like you're down to fuel, igniter, gas valve and the white (heat) wire. Now, I'm not one to discourage people from repairing their own units but, if you've replaced the circuit board and T-stat, I'd think you've already spent more than you would if you'd called a serviceman out. I'd do like Harold suggested, check the white wire and if it doesn't work, it's time to call for on-site help. It's possible that you have a safety holding you out of the heat cycle and you could inadvertently bypass this and create for yourself major problems.