I have changed the batteries in the remote, checked to make sure the toggle switches are in the same position in the remote and on the fan, checked the electrical switches and still neither the fan nor the light will come on. Any suggestions on what to do next before just replacing the remote?

Does your fan have pull chains and/or a wall switch? Does your remote have a small red light the lihts up when the button is pushed?

It does not have a pull chain or a wall switch. We cannot figure out where the LED red light should be coming from - we don't see a red light anywhere and I don't remember ever being aware of one when the unit worked. In the trouble shooting section of our directions it asks that question, but there is none shown on any of the diagrams of the unit. It is a Windward II by Hampton Bay.

Sounds like it is likely the remote. You can buy a Hampton Bay universal remote for $39 or an off brand for $29. Both should work and will require replacing the receiver in the fan housing.

Actually the Windward has a special remote, but it is more likely to be a receiver problem. In any case, since this is a fan with a lot of known issues, I would first get a voltage tester to confirm it is getting power. If it is, I would take the whole fan down, take it back to Home Depot, and get a different fan. Or if you really like it, exchange it.