For now, consider using an alternate FTP client like FileZilla to download the WP site locally. After that, attempt to set up a new site (not specifying any FTP info), just including the local path to the files you downloaded. Also disable any file synchronization and cache settings you may find (look around for them). Disable any contribute support, design notes, etc. See if you can just get Dreamweaver loaded with local files.
Just a site note, try not to work any more than you need to in design and especially split mode. You're 5 versions of DW old, back when standards compliance (much like all 3.9+ themes) did not exist and DW will have no idea how to render advanced CSS/HTML markup.
If you get it working like that, then duplicate the site and give it a new name in the Sites Manager. Edit that site and add in FTP settings. Try to connect to the server and work with it. If it dies on you again, delete the new site with the FTP settings. At that point there's some issue with the FTP connectivity. You might need to work on the HTML locally and FTP using FileZilla or whatever client you chose initially.
Do you have sufficient memory and hard disc space to run WP locally? A typical WordPress site contains approx 800 files in some 80 folders, plus an extensive MySql database for content. If you're using an outdated product like DW8, it's entirely possible that your computer isn't up to the task either. Something to think about.