I think it is an electrical issue. Did the furnace work from the thermostat before you switched it out? Perhaps your thermostat isn't wired properly to send a 12 v. signal to the furnace. You could check with a multitester. At the furnace, see if there is 12 v present and the fuse in the 12 v fuse panel is good.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI