I have a ceiling fan with a light kit, all controlled via a remote. One night I went to turn on the light with the remote (ceiling fan running) as I have done many times and the light bulbs burned out. I replaced the bulbs and they won't work, but the fan works fine.

I took apart the unit. I tested the blue wire (marked lights) with the 9-prong connector from the unit to the light kit off and I have power. As soon as I connect the light kit connector, I do not have power anywhere on the blue wire.

Thanks for any help!

The power readings can be misleading with remote kits. Sometimes when bulbs burn out they take the remote receivers with them. It is also possible you have a loose connection in the connector, you can try bypassing it for the light wire.

What make is the fan?

Harbor Breeze

Ok I stick by my original answer. If it was a higher-end fan I might have amended it.