Rth110b thermostat not calling for heat or turning on fan blower unit

Let me add to this: it is a 4 wire system. We replaced the old digital thermostat because the battery low thing was flashing even after we replace batteries and the auto setting would not call for heat. We replaced it with this rth110b from honeywell which will also not work on "auto" but does fine if we just manually set it to "on". Obviously this will not work for us, though, because we need the "auto" setting.

The problem may not be the thermostat, but the fan control on the furnace. Try this: disconnect "R" & "W" wires from thermostat, and connect together. Observe for the next few minutes. If the furnace starts/runs normally, the problem is relative to the thermostat. If not, post brand/model# of furnace.

We don't have a furnace... we have a hot water heater that goes to a hydro-air something according to my boyfriend but I thinks he's wrong because he doesn't know what he's talking about. We have oil heat and a boiler and a hot water heater and an air handler system with heating and air. I don't know what that adds up to

Definitely not garden-variety. Calling in a pro might be in order, to avoid creating a worse problem.

You may have a fan coil system. What were the old terminal designations or the model of the old stat.