We have turned the thermostat up but furnace will not come on. It sounds as though it wants to start then shuts down only to try again in a short while. The red light visible inside the furnace is flashing .I have tried resetting by shutting unit off at thermostat for a few minutes the turning on to heat mode.

possible stat failure

That's how it should work .Your furnace will cycle on and off to reach set point .
You don't have to troubleshoot the thermostat. The reason why your furnace cycle is once the heat exchanger get to a certain temperature the board will shut it off, fan would still work to cool heat exchanger down then once cool down furnace will fire up again .

Sounds like the heat anticipator in your thermostat is either bad or out of adjustment. Turn of the furnace power. Remove the thermostat wires from the thermostat. Turn the power back on. Connect the white and red wires together. The furnace should start up. Let it run a couple of minutes. Then disconnect the wires. The burners should shut off immediately. The blower will continue to run for 60 to 360 seconds then shut off. If this happens replace your thermostat. If the burners continue to burn, then your problem is either the furnace or the thermostat wires.

check that the replaced thermostat is the same temp degree setting of the last one

could be the thermostat sticking of the fan control afc not working sticking off on shut down thermostat sounds more like it

Sometimes a thermostat can accidently be put into C instead of Farh.
probably not the case though.

Souns like you have two furnaces in your house? Turn off the Furnace
if you are capable of removing the thermostat, check and make sure
no wires are touching-this can be the most common problem if a
thermostat has been changed out.

If that is ok go to the furnace giving you problems. Shut the power off.
Remove the furnace doors usually where the blower motor is there is a
control board. You are looking for terminals-R/W/G/C/ and Y.
Remove and cover the R and W wires seperate. Put doors back on
and turn power back on.If the furnace does not start up, then the
problem could be the thermostat or the wires.

To eliminate the wires or thermostat. Shut power off and remove
thermostat or remove wire from W. Turn the power back on if the
furnace stays off, replace the thermostat

can you manually fire the unit w/o the thermostat by shorting 2 of the 3 wires, there may be more wires than that, but you should be able to fire it on 2 to 3 wires alone let me know it sounds like something is floating voltage wise on the unit

first off buy yourself a honeywell stat, in my personal opinion lux stats are garbage, I have run into so many that are bad stats !!! but as far as your fan not shuting down, sounds to me like your fan center on your circuit board is bad and will not shut down the fan when needed, you will have to replace the circuit board, as the fan center is a part of the whole of the circuit board, hope that helps

Joss sounds like the anticipator setting on thermostat i would replace it with a digital it will be more actturat . The furnace has to go over temp setting to turn off

Hello Genna,
I am not a furnace guy but I may be able to give you a few ideas of things to diagnose the problem and get it resolved. First off, I assume you have a thermostat that you use to to turn your heat on. If it is a generic ( meaning : non programmable model) then you should be able to try this simple test. Remove the cover ( typically they snap on) around the thermostat so you can see the control mechanism inside. You should see few skinny wires ( similar to those used on a telephone wire) solid copper in various colors.. When you rotate the dial on your thermostat to call for heat, there is a small glass vial that has a drop of mercury ( which is electrically conductive) in it that makes contact and shorts two control wires together ad that is what calls for heat on your furnace. When the temp inside the room where the thermostat is reaches the tempertaure you requested, the bimetal mechanism either contracts or expands to reposition that glass vial to shift the mercury off the contacts and your furnace shuts off... That is the basics behind how your thermostat and furnace work ( generally speaking) If you can identify the two wires inside the thermosat that are shorted together when that vial of mercury shorts them inside it.. you can temproarily unhook them ( they are low voltage.. normally 24 Volts or less) so no worries about getting ashock or anything.. and short them together for a minute or two.. by doing that... your furnace should turn on and heat should flow.... Once you start your furnace this way.. unhook these two wires and your furnace should shut down .. It may take a minute or two ( depending on the control for it) If it doesn't..then your problem is on the furnace side and you may need to get the furnace control system serviced or replaced.. if it does shut down, then your problem is your thermostat and thats a simple replacement.. Also.. make sure the thermostat was properly leveled on its base.. The position of the thermostat ( meaning level) will dictate when that mercury makes contact and your furnace switches on.. OK..I tried to explain the works of this to you but here is a link to a Honeywell site that explains it in simpler terms.. The part about shorting the two wires together and then opening them will aid you in identifying where the problem actually is.. here is the link: http://homerepair.about.com/od/heatingcoolingrepair/ss/thermostat.htm

Hope this helps you more than confuses you..
Regards