I bought a home with a new Carrier hi efficiency gas furnace but the old original White Rodgers theromstat. The original thermostat is the mercury switch type for both heat and cool and has 4 wires (Red, White, Green and Black). I tried to install a new Noma #52-2570-6 digital thermostat, which shows the 4 wire wiring scheme as G (Green), W(White), RH/RC (Red) and Y (Yellow). So I wired the existing control cable Green-G terminal, White-W terminal, Red-RH/RC terminals and Black wire-Y terminal. It does not work at all even for turning the Fan on manually or turning on the heat.

Any ideas?? :(

Go to the furnace, and see what the black is connected to. If it is not the Y terminal, disconnect it from the Y terminal at the thermostat. While you have the furnace open, check for a blown fuse inline to the transformer or on the control board. If the black was connected to the common or the transformer, and you connected it to the Y, and turned the thermostat to cool, you would have a direct short across the transformer output. You can use a black wire to control the A/C, but both ends need to be connected to a Y terminal.

If you still remember the where the 4 wires were connected to the White Roger thermostat, take note of the name of the terminals the 4 wires are connected to. That may help as sometime the colour of the wires are not always correct.

Or you really want to test it out:
Connect RED wire to GREEN wire should turn on the fan
Connect RED wire to WHITE wire should turn on the heat

Did you disconnect the power at the furnace first? Maybe you blew a low voltage fuse.

Make sure you increase the heat setting to go above the room temperature.

Thermostat wire color codes explained.
Please note. Not all installers use the proper color codes when they install or replace equipment. It may be necessary go go to the furnace or outdoor unit to verify what wires are for what purpose. Also be sure there are no splices in the wire that could change the wire colors between components.

R (red) or Rh (Red heat) 24 volts from equipment.
Rc (Red cooling) 24 volts from transformer in cooling equipment.
Note: If only furnace has a transformer and cooling equipment does not jumper Rc and Rh.
W (White) sends 24 volts to furnace control to start the heating cycle.
W2 (no standardized wire color, usually whatever wire color is available) controls second stage heat.
Note: W2 is most often used for heat pumps to control what is called emegency heat or Auxiliary heat, and most often will use the white wire.
Y (yellow) often (blue) is used, controls cooling unit (outdoor condensing unit) also is used for heat pump heat.
Y2 (no standardized wire color, usually whatever wire color is available) controls second stage cooling.
G (Green) controls the fan "on" operation of the furnace/air handler. Also often is used to start the blower for many electric furnaces.
C (common) most often brown but can also be black or other color available to installer.
O (orange) Energizes heat pump reversing valve for cooling (Trane and most other brands).
B (Blue) Energizes heat pump reversing valve for heating (Rheem, Ruud and Weatherking).

My thermostat randomly reprograms itself to 64.7oC
The digital display is also VERY faint when I try to go through the PROG cycle. It is brighter when it is just on the current reading.

any ideas?