When you click on the index.html file in local publish can you navigate your entire site? Is everything there? No missing bits?
If your answer is yes, then you can use a 3rd party ftp program to upload the contents of the local publish folder to your hosting environment.
Chances are you are on a linux host so I will post my tutorial for hooking up and uploading to my Red Hat servers. You will need to ask your host what you need to use for credentials and file locations for your web hosting but this tutorial should get you started (even includes a link to download a copy of FileZilla).
http://www.gotfusion.com/tutorials/tut.cfm?itemID=4066
Most web hosts understand FileZilla so you should have no problems asking your host to help you out with the setup you need to connect and upload.