I currently have a Honeywell T874C1000 and want to replace it with a programmable thermostat. It controls a cooling only air handling unit with an outdoor condensing unit. No heat.

Here are some options:

Honeywell Home Non-Programmable Thermostats: These thermostats are designed for simplicity and comfort control. They come in a range of models, from the classic circular dial to easy-to-use soft-touch buttons and backlit displays. You can easily set your preferred temperature with the touch of your hand. The Honeywell Home website has a range of non-programmable thermostats to choose from .

Honeywell Home Programmable Thermostats: These thermostats allow you to set different temperatures for different times of the day. This can help you save energy and money on your heating and cooling bills. The Honeywell Home website has a range of programmable thermostats to choose from.

Honeywell Home Digital Non-Programmable Thermostat RTH5160D1003/E: This thermostat is simple and intuitive to use. It has a backlit screen and basic button functions that make it easy to control the temperature. Once you set your desired temperature, the thermostat stores it in its memory, even during a power outage. Non-Programmable Thermostats ' Honeywell Home RTH5160D1003/E Non-Programmable Thermostat ' Honeywell Home Might as well look at the programmable ones on their site. Check their customer service if you have an additional question. The above mentioned should work with your setup.

In all likelihood the thermostat has failed. Replace it.

Match the thermostat wires to the letters on the new thermostat terminals R Red Y yellow ETC.

Probably not. There are replacement models available.
The T6661B programmable room thermostat is also known as CM61.
CM61 1 day wireless programmable thermostat is replaced by CM921.
CM61 1 day wired programmable thermostat is replaced by CM901.

On that thermostat there is an R and an RC wire connection, the R is the power wire for heat and RC is the power wire for cooling. If you connected the power wire (normally red in color) to the RC only the fan control and AC control will work, there has to be a jumper wire between the R and RC terminals (assuming there is only one control transformer) for both the heat and cool functions to work.

Strange. Does the thermostat control both the air conditioning units and the furnace. If not make sure the furnace thermostat is turned down to below 65 degrees.

check to see if the B terminal is on the new t-stat if connect to it , but this terminal refers to heat pumps and is normally use to energize the reversing valve on the outside unit and not used on ac units , but normally the tag O/B is the same terminal on therostats

Sounds like it may have lost power. Check the breaker and the fuse at the furnace. If they are all in the on position and working then it sounds like you may need a technician. If the display is blank on the thermostat you may also want to replace the batteries.

what type of system do you have? cool/gas heat, heat pump, electric cool & heat. split system or package unit?

the analog unit uses just two wires for heat. red - white. there is a heat anticipator setting that must match the burner current. check your programmable specs and follow instructions.