A technician usually starts with safety: a carbon monoxide reading near the appliance and vent, a look at the flue, and a check for water damage on the burner and controls. Only then do they chase the fault itself, such as an igniter, a flame sensor, a pump, or a blown control fuse.
A quick repair usually doesn't need a permit, but replacing a boiler or furnace does. In Pembroke, gas and sheet metal permits are filed online with Building and Inspectional Services, and inspections are booked for the next day or the earliest opening, so a full replacement is rarely finished in one night.
Expect the contractor to explain whether a temporary fix will hold until a planned replacement. After a flood, ask for that advice in writing in case you file an insurance claim.