Have you tried creating a new WebLogic user with Admin rights? Are you sure that there isn't an "overlap" of granted roles? As it sounds like you've granted the original user with all permissions possible. I'd suggest creating a new user and just granting the new user with the top level WebLogic admin roles and see if this makes any difference.
I did as you suggested and created a new user
Added it only the BIAdministrators group - same result: Administration link does not display, no folders under the Shared Folders display and the "Permissions" does not show in the "Tasks " (not that it is grayed out, it just does not show)
Added BIAuthors - same
Added BIConsumers - same
I would suggest looking at the catalog in offline mode and checking the permissions there and ensuring all is OK.
Please mention the version of BIEE you are using.
From the name of the roles, it looks like you are on 11g and since you are getting "Access denied to user to path" , it looks like a GUID mismatch or lack of catalog validation issue
OBIEE 11g: How To Refresh the GUIDs and Perform a Web Catalog Validation - Cluster/Scale-Out - the Reasons to do it, Preventing Inconsistencies and Process Detail (Doc ID 1493912.1)
Remember, its valida if you are on 11g.
Added it only the BIAdministrators group - same result...
Don't you have any other app roles than BIAdministrator, BIConsumer, BIAuthor? Because those are just the out of the box application roles, but doesn't mean they are really used accordingly to their names.
In a real environment I would expect these 3 to not be used or just be there as references, but to have many more application roles to define the real security.
You would need to look into the document describing the security model setup to find out what is really needed to be an admin.
Right now in your environment you aren't really admin, you don't have any other access than a quite generic BIAuthor I would say.