Linda,
It seems you have to select the lines one by one using shift+click. Then
click on the contextual format tab, click dialog starter button in the Shape
styles group, choose a style to your liking. Or click the shape outline
button and choose a totally different color, thickness and so on.
In PowerPoint 2003 you could select all the connector lines using the org
chart toolbar, but to the best of my knowledge this has gone in PPT 2007.