It looks like the tabs are working when you press the forward/back buttons, but the main pane area isn’t moving. Have you tried a minimal example page, without all the other tons of JavaScript you have on the page? I think it might be something simple, and there will be a palm-forehead moment for you, but I can’t see the problem from here.
Try to build the effect with just colored empty HTML boxes for the panes, to see if you can make it work in principle.