It appears that all was successful except the Telerik installation. My "guess" is that the Telerik installations for v 05.04.04 and v 5.05.00 had also failed during previous upgrades and their packages did not get automatically removed so tried unsuccessfully to install again.
Please check the file/product version of the Telerik.Web.UI.dll located in the site's /bin folder. For DotNetNuke version 05.06.02 it should be: 2010.03.1317.35.
Please check the binding redirect for the Telerik.Web.UI assembly in the site's web.config file in the <runtime><assemblyBinding> section. For DotNetNuke version 05.06.02 it should be:
<bindingRedirect oldVersion="2008.0.0.0-2020.0.0.0" newVersion="2010.03.1317.35" />
Most likely, an older version number will be found.
If the site is not down completely and when logged in as host user you can run the Install Extension Wizard from Host --> Extensions page I would then try the following:
1. Delete any Telerik_xx.xx.xx_Install.zip package from the site's Install\Module folder.
2. Use the Install Extension Wizard to manually install the Telerik_05.06.02_Install.zip package (extracted from the DotNetNuke 05.06.02 Upgrade package's Install\Module folder.
If it successfully installs, that would be great! Otherwise, we'll at least get a more detailed error message as to why the Telerik assembly is failing to install correctly.
Let us know what you discover.