Identifying active database links

Hi All, we have over 500 DBs in our company and they are from 9.2 to 11.2. I've been asked to identify the database links that are NOT functional anymore and are NOT PUBLIC DB links. I'm able to validate the DB links that are PUBLIC but for private DB links I need to provide passwords which is impossible to provide because we don't keep track of personal passwords. People have left the organization as well and their ids are still there.

I've to run the query like   

SELECT USER FROM DUAL@NAME_OF_PVIVATE_DB_LINK  to prove if the DB Link is working or not.