If you have changed up the connection file to make use of your live servers db info then that is all that you should need to change. The site should function if it is uploaded to the root of your live server.
If you are getting errors with files referencing the c drive then then your local site might not be defined properly. The links in the site should not use file system paths but local site relative paths. How do you have your local testing site setup? You need to have the local info and testing server info setup and pointing to the correct locations. You normally only see the file system paths if the structure for the site is not defined properly in your site settings. Here is link to a doc that we have on setting up a DW site: