Webpage Not Displaying As Programmed

During a routine theme update two days ago, our webpage suddenly stopped responding to almost all programmed settings. The home page displays with almost all pages, and nothing looks like the theme is programmed to.

Bullet points:
– Theme update was unsuccessful based on missing stylesheet program, so old version is still active.
– All menu, settings, reading, page content, etc, appears exactly in our areas of wordpress. Nothing appears the same on the webpage.
– Page address is http://www.globalteachingexchange.com .

Any help would be fantastic!