It sounds like you may have published your site to a different location than the default wwwroot folder. By default, when you use Web Deploy to publish a site to a local IIS instance, it should publish to the wwwroot folder. However, it's possible to change the publish location during the publish process.
To find out where your site was published, you can check the publish settings in Visual Studio. Open your project in Visual Studio, right-click on the project in the Solution Explorer, and select "Publish". In the "Publish" dialog box, select the publish profile that you used to publish your site. Then, click the "Edit" button next to the profile.
In the "Connection" tab of the publish profile settings, you should see a "Destination URL" field that specifies the destination server and site. The "Site/application" field should specify the virtual directory where your site was published. You can click the "Test Connection" button to ensure that you can connect to the destination server.
Once you've found the location where your site was published, you can check the IIS settings to ensure that the virtual directory is configured correctly. Open the IIS Manager and navigate to the site where your virtual directory is located. Expand the site and find the virtual directory. Right-click on the virtual directory and select "Manage Virtual Directory" -> "Advanced Settings". In the "Physical Path" field, you should see the path to the folder where your site was published.
If the physical path is not correct, you can change it to the correct path. Once you've made the changes, you may need to restart the website or the application pool to ensure that the changes take effect.
As for publishing to GoDaddy, you should be able to use FTP to publish your site just like you did with VS2010. However, make sure that you use the correct credentials and settings for your GoDaddy account. You may want to test your FTP connection first before publishing to ensure that you can connect to the correct server and directory. Also, make sure that you have a backup of your production site before making any changes.