Orman-
I know many failures are due to a bad hose to the expansion tank or a bad hose connector weld atop the boiler tank, and many owners don't check the boiler tank level, just relying on the expansion tank. However, if the float switch is in the boiler and not the expansion tank, and Roland bypassed the switch with still the same result, would that not imply something else wrong?
If it is the board itself, and the switch is a normally open one that closes when the level is okay (which is why you can jumper its board connections to bypass it if it's faulty), then I'd first suspect a short on the board along that printed circuit. But I commonly find micro-cracks (nearly invisible splits) in solder points to be a culprit on all kinds of pcb's; a cursory exam won't reveal those - I have to carefully check each solder point with my OptiVisor magnifier. I used to think micro-cracks only occurred on pcb's that heat and cool cyclically, but I've found them in things as inocuous as a wireless mouse. A simple remelt of the cracked solder point is a cheap fix... if you can find the break. I'd start from the board connectors for the float switch and work from there.
Nevertheless, it certainly could be something else.
But, Roland, did you reset the unit after you jumpered the switch connections, flipping the inside switches off for a minute, then back on?
Joel