We recently moved in to this house and it has a forced-air gas furnace in the basement but on the roof is the air conditioner. It is refrigerated air (I don't know the brand) and it has its own blower and its own duct-work in the attic so the two systems operate independently - the cooler doesn't use the fan from the furnace like our former home.

The thermostat is an old mercury-type with the brand name of White-Rodgers. When I pulled it out from the wall there are two cables - one seems to be coming from above so I presume it's the AC. There are only two wires in each cable; one red and one yellow from each for a total of just 4 wires. No other color codes, no nuthin'.

I have a new digital thermostat but it has 7 connections marked G-O-B-Y-W-RC-RH. All I have to work with are the two pairs of red and yellow wires. No COM but there is a blue wire coming apparently from the furnace and that blue wire is not connected to anything.

First off, you will want to kill power to both units while wiring the new stat. Next, take the red wire from the cable that you think goes to the roof a/c and put it on RC (make sure there is NOT a jumper between RC and RH, remove if necessary) and the yellow wire in that cable to Y. Then take the red wire in the cable that you believe goes to the furnace and put it on RH and the yellow on W. This should get you up and running. Test to make sure cool setting kicks on a/c and heat kicks on the heater. If things are reversed, simply swap the cables. Please let me know how things work out.

PS. This is assuming that both units are indeed controlled by the one thermostat.