The online journal system at my university does not always give accurate information as to whether a full text article is available, sometimes it says it is, only to find out that its not, and other times, it says there is no full text article, but in fact, there is. I usually google the article title and author, if the library system does not indicate access, and try multiple web searches on both google and google scholar to see if there is another means of access.
Logging in directly to some of the sources, such as Ingenta or Heinonline, Wilson, Ebsco, etc. seems to be the best ways in some instances in figuring out if there is in fact full text access.