Does anyone know how to I may have turned off the algorithms and inputs tool menus in the modeler? I have not been able to figure out how to get it turned back on.
I'm not sure how this happened in your case, but I was able to make the panel disappear and reappear by using the "splitter". This is a thin vertical bar that usually separates the algorithms panel from the model panel. They can be quite difficult to see on some operating systems.
Hover the mouse just to the left of the big white panel, just inside the window border, and the mouse pointer should turn into a two-way arrow cursor (<-> on Ubuntu)
Clickand drag the pointer to the right and once you've moved it far enough to the right, the panel should (hopefully) pop back.