Another cause for the module not to activate besides the permissions over the App_Data folder is if the module is imported as a structure from another site where this module was present.
The import of the module completes with success, but the activation fails in this scenario where the imported module is using a classification selector which selects from taxonomies that are not the default Categories, Tags and Departments, but a custom one. When the module gets activated it will search for the custom classification added in the original site where the site was used and if it doesn`t find it this error will be thrown.
Another cause is if manual updates have been made in App_Data/Sitefinity/Configuration/DynamicModulesConfig.config which have removed/modified a section of the configuration that is required for the module to start.
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