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..