I cannot switch off the heater. Regardless of where I set the thermostat [55 degrees, Span 2], the thermostat in the basement fires up the boiler - the thermostat on the second and third floor work fine. The end effect is that the temperature in the basement is around 77 degrees.

What do I need to do to get the thermostat to just fire up the boiler when the temperature requires it?

You may need a new thermostat if W and R are shorted in thermostat. Check the wires to make sure it isn't the wires shorted out in low-voltage wires.