Looking at the image, I'd say the breaklines have been added. You can see this in the triangulation and the blue breakline lines. However, you need to specify what the breaklines will do.
I am guessing that your area represents some islands in a lake. In which case you may prefer to use hulls rather than hard breaklines (same dialog box, just a different option). You can also set the polygon type of the lake areas. Try using 'Replace Polygons' for the lakes. In my experience, water areas need some intervention like this. Check out the ArcGIS 9.3 help for TIMS here: http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=Creating%20TIN%20surface%20data%20from%20vector%20data