For the site where this problem occurs, please find its media directory and change the permissions as I described. In your /blog/ installation the path to the media directory will be —of course— /blog/media. If the problem only happens in the /blog/ site, then you may have to generate .htaccess files for both the site at the root and the one in the /blog/ directory using Admin Tools. The reason is that, unlike Joomla! configuration settings, the .htaccess settings are inherited from the parent to the children directories, which means that if there is an .htaccess in your site at the root it might block access to media files in the site inside the blog directory.
As a rule of thumb, it is an extremely bad idea having one Joomla! site in a subdirectory of another Joomla! site. The best solution is using subdomains.
Nicholas K. Dionysopoulos
Lead Developer and Director
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