If the blower fan does not work in the "fan only" mode (or any mode), does it necessarily have to be replaced or could something else be wrong?

It could be a relay and today many of those relays are on a circuit board.

It could be the low volatge transformer or a fuse on the circuit board.

It could be the fan motor or fan motor capacitor.

It could be the circuit breaker is off or the switch for the furnace.

There is a lot to choose from.

Does the A/C unit outside come on?

Does the furnace come on?

The circuit breaker and furnace switch are on, the furnace appears to come on, noise is heard but the blower does not come on.

You will need to check the other items I posted.