It's clear now that the upgrade of the HTML module failed to complete as DNN versions 05.01.02 and later should not have an App_Code\HTML folder nor have more than a few files in the DesktopModules\HTML folder. Let's try the following:
1. Completely delete the folder HTML from the App_Code folder.
2. The DesktopModules\HTML folder should contain the following files (all of which should have as their modified date that of when you did the FTP upload):
\App_LocalResources\EditHtml.ascx.resx
\HtmlModule.Ascx.resx
\MyWork.ascx.resx
\Settings.ascx.resx
\SharedResources.resx
\Providers\DataProviders\SqlDataProviders\03.00.00.SqlDataProvider
\03.01.00.SqlDataProvider
\ . . . (8 other files all ending with .SqlDataProvider extension)
\05.01.04.SqlDataProvider
\05.02.00 SqlDataProvider
Uninstall.SqlDataProvider
\EditHtml.ascx
\HtmlModule.ascx
\license.txt
\MyWork.ascx
releaseNotes.txt
Settings.ascx
Note that there should be NO files with a .vb extension in the DesktopModules\HTML folder or in the SqlDataProviders child folder. Delete any files from DesktopModules\HTML and its child folders that are not listed above.
Try to access your site following the deletions. If we are very lucky, all Html modules should display properly. It is quite likely, however, that the failed installation also resulted in upgrades to the SQL stored proceedures and/or Tables relating to the HTML module or the module's definition failing to complete. If that is the case and provided you can access the Host-->Extensions page we can take a look at the registered definitions for the module and then try to reinstall the Html module itself with the repair option selected.
On Edit: I also meant to add that your web.config is correct as there should be no entry added to <codeSubDirectories> for the HTML module.