Perhaps this could be a web browser incompatibility, or possibly a javascript error stopping the items in the ribbon from being enabled. It might be worth checking access using Internet Explorer.
Also useful to check for any javascript errors during the page load - which could prevent the menu from being rendered properly and the icons being enabled, or looking for other error messages information in the web browser development tools console.
I have recently seen similar problems with disabled toolbar in SharePoint 2010 when browsing using Safari 7.0+ on OS X. Some icons in the toolbar remained disabled when Safari was upgraded to Safari 7.0/7.1 on OS X, and several AJAX features stopped working.
A workaround for an individual user using Safari could be to use the Safari developer menu to send a different 'browser user agent'. See 'enable developer tools' in Safari preferences.
For a server side fix - look at this answer to 'iOS 8 / Safari 8 not working with ASP.NET AJAX-Extensions'. The ribbon in Sharepoint uses 'ASPMenu' from the .NET framework, and some functionality can be restored with an update by fixing the way that .NET recognizes browser capabilities by an extra custom .browser file alongside the existing compat.browser file.
For a more complete server side solution - fixing the browser compatibility, see also
iOS 8 / Safari 8 not working with ASP.NET AJAX-Extensions