The fan works using the remote, but the light doesn't. I've tried using the remote from another similar fan that does work with the remote on the non-working one, but that doesn't work, either. This is a Harbor Breeze fan with a remote and no pull chains.

Have you tried to contact Harbor Breeze tech support?
How old is this fan? Is it under warranty?

Did you check the light connection at the ceiling or the bulbs?