Running Ethernet Cable through Walls?

[Frac]

Do you have an interior wall in the same place above and below?

Interior is important because no insulation. Cut a small rectangle upstairs about the size and location of a 1-gang old work box. Use a 1/2? auger drill and extension to drill through the hole at a slight angle through the bottom plate of the wall.
Directly below that spot downstairs, cut another hole for a 1-gang old work box. Fish a weighted string down the wall and catch it in the basement cutout. Use that to fish your wire.

If you can do that, worst case you put a wall outlet on each hole and run patch cables to and from.

ETA: to run through duct work, get ?Plenum? rated cable.