Most but not all of the ejournals available from the library are included in the Serials Solutions ejournal list. Use this resource if you already have a citation to a specific journal article and you want to know if that article is available full-text online.
Retrieving your article is a multi-step operation. For example, suppose you want to read "The meaning of 1 Corinthians 12:31" by Willem Unnik in Novum Testamentum, volume 35 (April 1993), pages 142-159. Then you would proceed as follows.
Here is the main ejournal list.
If you don't find what you want there, then also check the alternate ejournal list from TDNet that lists all resources available through TexShare.