This repair guide provides a procedure to test the Steam thermostat switch (attached to the boiler). No need to disassemble, just requires a multi-meter - [guide|101729].
There are very few components in the steam circuit - it will likely be either the 125 deg. thermostat or the micro switch attached to the steam valve. Opening the steam valve should turn the pump on. If not, the problem will be related to the micro-switch wiring, or possibly the cam that operates the switch when the valve is opened may have just come loose and is not turning the pump on.