Lighting, Light Fixtures, Ceiling and Exhaust Fans - Wacky Wiring Problem

I took down a light fixture to put up a ceiling fan. I've hung fans all over the house and never had a problem until now. When I took down the light there was a black/white wired together. I have the blue, black, white and ground from the fan. From the ceiling I have 2 black and 2 white with the ground. This is counting the black/white wired together. On the white wire from the ceiling I can touch the white neutral from the fan to it and light comes on. If I touch the white from the ceiling to the black fan wire then the fan comes on.
I have the blue fan wire connected to the black ceiling wire while this is happening. Bottom line is I can get one or the other to work but not at the same time. This is going to be controlled by a single wall switch. It's a harbor breeze fan.

Thanks for any guidance. I've already spent too much time on something that should have taken less than an hour.

James

Clarification. Tell us exactly the configuration of the wires from the ceiling box, and only the termination parts, and if they were capped or not. For instance black/white capped, black, white, ground.

Does this switch control any other light in the room? If not, two cables in the ceiling box indicate a switch loop.

The fan wires should be connected to the same wires as the light fixture was if you want the switch to operate both the fan and the light.

If you want the fan to work off the pull chain, attach the fan black to the black and white that are connected together. Connect the fan light wire to the black that was previously connected to the fixture black.