We are currently running a modified version of jShowOff, a jQuery slider. It has never been modified since it was created back in 2009 and lacks a few features we need. I have been searching the latest crop of sliders and haven't found one with the features we need.

It must show a transparent panel over the left 20% of the slide image that contains up to four text headlines. The slider will transition between four images related to each headline. When you click on a headline, the slider jumps to that image and highlights the headline text. Clicking on the image takes you to the linked URL.

So far, nothing out there that shows multiple text elements over the current image.

It's sounds a little specific to me, I don't know if you'll find something ready out of the box.

But there is not only JQuery, there's a lot of others JS frameworks that you might want to look into. Some examples:
ExtJS
YUI Library
MooTools
Prototype

But if you don't find it, you'll have to build it.