I successfully installed DotNetNuke DNN 4.8.4 on a Godaddy "free" (Economy) account that comes with the domain name. All you have to do is carefully read the forms during the installation. Please read the post to the end before attempting to install.
The installation was very straightforward:
Use the hosting control panel to create the database. I did not check the ASP Schemas or DSN boxes.
In the file manager, the root came with only a view permission. Select it, click permissions from the top and check "Applications Have write Permission."
On my vista basic machine I right clicked the Install zip and removed the "Archive" property (I'm not sure if this was necessary but i got problems before related to properties of the archive on my Windows server 2003 machine). I used the FTP in windows explorer to upload the installation zip. Then I used the File Manager on Godaddy to unzip it.
I edited the web.config to include the database name. I used the editor in the file manager so as to avoid any potential permission issues using ftp. I replaced (local) with the database URL from the SQL manager, it looks something like sitename.db.#######.hostedresource.com. Remember that the database name and database user name are the same, it says so on the form you use to create the database (as I said read carefully).
I then browsed to my URL and selected Custom Install and wen throught the wizard as usual. I tested the folder permissions and database connection before proceeding. In my Installation I did not select any additional modules to install, I don't know if that would affect anything.
Now ... If you are using the free account you are likely to have problems with postback buttons (like updating the site settings). I think this is related to how godaddy inserts the big ad at the top. I've made a separate post on this you can check for a resolution here http://www.dotnetnuke.com/Community/Forums/tabid/795/forumid/107/postid/333072/scope/posts/Default.aspx
I think if you use the paid Economy account with no ads it should work. Please check the post above or a later post in this thread to see if anyone confirmed that it works properly with the Paid Economy account. And if you manage to confirm that it works properly yourself (by sucessfully installing it on an Economy plan) please update this thread to help the apparently large number of people trying to install on Godaddy.
Remember to check that you can update site settings and install core modules before updating this thread.