Alright, so I uninstalled blender and reinstalled… maybe something was wrong… So I thought…
So after installing and opening up a new blend file, i deleted the cube, put a plane down, extruded a vertex, selected two vertex’s and pressed the “f” key and it still wont work.
if you selected two vertices and pressed ‘f’ and got the result in the image in your previous post, blender is working just as it should. To create a face, you need to select 3 or 4 vertices, then press ‘f’
Post a blend that shows this problem, so much easier to help than just with images.
Also try File / Load Factory Settings to revert back to the blender default settings.