The board chatters when the thermostat is off, and the heater will not work, model number50a55-571

Might have a bad relay in the circuit board,which means replacing the board, but you say the thermostat is off,furnace not going to work with it off

When the furnace is turned on it will not run, the exhuast motor does not start and still chatters intermittingly. The fan will run when swithched to on and the a/c also appears to work. Checked for power at the exhaust fan and when heater is switched to on I see no power at fan. Most of the chattering on the circuit board takes place when unit is swithched to off.

Have ou checked or found a plug in type automotive fuse in the circuit board,, it sounds like you might have to replace circuit board, its hard to say for sure without being there, it might pay you to call out the hvac tech, to keep you from buying unneeded parts and it still not fixed