I'm having trouble getting slideshow plugins to show up in my header. I want to have a slideshow of featured posts show up in the header of only the homepage...

Which plugin did you try and what did you do to display it? Featured Content Gallery should work althugh a few users reported problems. These plugins usually use Javascript frameworks and different ones often don't work well with each other. Try finding a plugin that uses jQuery instead of Mootools or Prototype/Scriptaculous because jQuery is the Javascript framework of choice for Wordpress and Atahualpa also uses it a bit. (Featured Content Gallery is Mootools)

The plugin I've been trying to get to work is vSlider...what plugin would you suggest to create a slideshow with cross-fade/transitions where each image is linked to a particular post/case study?

I have not used any myself but users have. If one doesn't seem to work, try with the Default theme, also set Javascript to external in Atahualpa, disable plugins on by one to track it down to a specific theme/plugin/configuration