OK, this finally worked.
Not sure what was going on with WP version 3.4.2. At the end, a few widgets got imported.
I then updated to WP 3.5 and noticed I had a plugin that was causing the widget areas to be unavailable/uneditable. I disabled the plugin and imported the file once again. As I had tried to import the file several times before, this caused the widgets to be duplicated/triplicated in the same widget areas. So, I deleted manually all widgets, imported back the file and now all is OK. All widgets were imported but one I'm using on my home page, I guess because that widget area is specific to my theme.