I would first eliminate your wall thermostat as the issue only if the inducer will not even start up on the call for heat. Jump out the red and white wires that connect to it either at the t/stat or at the furnace end if the inducer does not run as explained. The furnace will start up. If it stays running then the t/stat is bad. If the flame goes out after starting then you have flame sensing issue, so that sensor could well be out again as a gas valve is typically going to open or not.
Where do I find the flame sensor and what does it look like? Not the igniter as I already replaced that.
The flame sensor is part of the ignitor assembly -you said you replaced it in your post. Make sure it is clean and in the flame. Use some steel wool to lightly buff it.
Cleaned sensor. Turned furnace back on, flames lit and ran for several minutes. Flames shut off, but fans keep running and blowing the cold air continuously. If I flip the main switch on the side of the furnace off and back on, the system runs normal for several minutes. Again, the flame goes off and fans continue to run. The blower does not shut off for quite awhile, if at all.
This may be a flame sensing issue or a problem within the mechanical part of the valve. The gas valve provides the flame sensing on this unit, so with the problem being the flame sensing then it looks like you need a new valve regardless of what is internally wrong here. The valve is probably pretty costly and there may be a retrofit kit made that you can install as this is getting old. You should have 24 volts being sent to that valve on the call for heat between terminals 1 and 3 on the 4 wire connector per the schematic that I see. This would prove that the board is fine.
Is there any way to take the valve off and test it?
OK, we'll go from here. Thanks for your help.