" wrote:

Click from where, the furnace or the thermostat?

I don't get the click from the thermostat.

So take your meter and see if you have control voltage from the furnace
wires to the thermostat.

On a digital thermostat the batteries only serve to run the thermostat
electronics and maintain it's program memory, the control voltage
provided from the furnace is what operates the relay in the thermostat.

The control transformers on furnaces sometimes fail, sometimes just the
wiring from the furnace to the thermostat fails, sometimes the
thermostat itself fails. The fact that the display on a digital
thermostat seems to be working ok is no guarantee that the thermostat
has not failed.

If you get control voltage on the wiring to the thermostat (you should
be able to measure on the sub plate with the thermostat removed) it is
possible to manually short the appropriate connections to test the
furnace since this is all the thermostat does.

The wiring colors can be all over the place so if you have the manual
for the thermostat you should be able to find a diagram showing it's
connections with more descriptive language. In a simple heat only setup
there might be only two wires, a control voltage common and a heat wire.
For a heat / cool forced air setup a control voltage common, a fan wire,
a heat wire and a cool wire would be expected. It doesn't get
complicated unless you have a heat pump with reversing valves or
similar.

This link: http://home.howstuffworks.com/home-thermostat.htm has a
pretty good description on how a thermostat works and includes the
following description of the normal connections to a thermostat:

RH - This wire comes from the 24VAC transformer on the heating system.
RC - This wire comes from the 24VAC transformer on the air-conditioning
system.
W - This wire comes from the relay that turns on the heating system.
Y - This wire comes from the relay that turns on the cooling system.
G - This wire comes from the relay that turns on the fan.

If you measure between say RH and W with a meter you should read 24VAC
or close to it. If you jumper from RH to G the fan should come on,
jumper from RH to W and the furnace should come on (you should have the
fan on first). If these tests work the problem is in the thermostat, if
not the problem is further down the line.

Pete C.