If you already have a dampness problem then I highly doubt a "stick-on" system will do much good.

I would either try using a sealant, much like Thompson's water seal, or do what I did, which is UCoatIt. It's an epoxy floor covering that's pretty much impervious to anything you'll likely find in a garage. Even brake fluid and battery acid won't touch this stuff. It can be a little pricey, but you'll never have to do it again.

UCoat It Epoxy Floor Coating