I’ve found that 9 times out of 10, a 404 for a direct link to a file is because the file isn’t actually there.
Try placing a text file (or html or whatever) in the same directory as your css file and see if you can hit it with a browser (by copying/pasting the URL to your css file and just replacing the filename). Be very careful to make sure you’re visiting the same directory during this test. If you can’t get to the test file, you’ve got the wrong path altogether.
If you’re on Apache, it shouldn’t be a permissions issue. You’d get a 403 rather than the WordPress 404. I’ve seen this be a permissions issue on IIS though. If you’re on IIS, right-click on the file, go to the security tab, and make sure the ‘everyone’ user has full control (just as a test). If this fixes your problem, it’s a perms issue, and you’ll have to figure out what level of security to scale back to.