This can be caused by a number of things, here are a couple items to check...
1. Browser cache. Especially in Chrome, make sure to clear the browser cache after uploading your site. Hit F12 to open Chrome's developer tools, then click Network and place a check by Disable Cache. Leave the dev tools panel open and reload the page. If it was the cache, you will see your updated site now.
2. The Root Directory field. In DW, go to Site > Manage Sites. Click the site you're working on and hit Edit. Go to Servers > Basic and verify the Root Directory (usually htdocs, public_html or www) is filled in. Second, make sure that folder DOES NOT appear in your Files window. If it does, it would mean you've accidentally introduced a duplicate site where you would be uploading to yoursite.com/rootfolder instead of yoursite.com.
3. For the computer you can't connect with, try exporting the site from the "good" machine. Go to Site > Manage Sites. Click on the site you want to duplicate and click Export. This will create a .ste file of your good site's settings. Copy that .ste over to the "bad" computer and go to Site > Manage Sites > Import to bring the exact settings over. Test the connection. If it still doesn't work, it points to an issue with your network hardware or security settings vs a DW issue.