Th e first thing I would recommend doing is to remove the cover from your thermostat and the three or four screws that secure base to the wall .Check to see that all wires are hooked to proper terminals. On most t-stats the R.c and Rh should have a jumper wire And red hooked to R.
To make sure you did not get a bad t-stat I would dissconnect all wiring from t-stat after noting how it's wired now. Then I would hook red and white wires together.This should
turn your futnace come on and run. If it does then I would just get t-stat exchanged.Hope this works for you. Good luck and thank you.