Does Paint Seal a Concrete Floor?

The first thing I would do is grab a piece of tin foil, and tape it to the floor with duct tape on all sides, so it's sealed. Check it in a day or so. If it's damp then I really wouldn't recommend carpet at all. Have you ever has a leak in the basement? If you see white mineral deposits on the walls or floors there is a good chance you have moisture issues. Sometimes a heavy duty dehumidifier does the trick if you have no leaking. To fully seal the floor you would have to take up all the sealant from the old carpet. Most water proof sealing has to be cured to open up the pores of the cement and the waterproofing paint goes into those pores to make a secure bond to keep out water, but typically this is done only on walls.

Paint doesn't really seal the cellar floor. If you have moisture coming up through the floor, it will peel the paint. The way to seal a cellar floor is to wash it, let it dry, etch the concrete and apply urethane paint.