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Below is a photo of my current thermostat's wiring. I have a few questions:
The jumper is installed between Rh and Rc, because your setup does not use two transformers. Rh is powered from the heating system transformer, while Rc is powered from the cooling system transformer. However, it's common to only have a single transformer for both systems. In which case, the jumper between the terminals may be required.
The only way to tell if and where the blue wire is connected, is to open up the furnace or air handler and have a look. Without knowing the exact model unit you have, it's not possible to tell you exactly what to look for. Basically you'll want to follow the thermostat cable, and try to locate where the wires terminate inside the unit.
