For some reason, I can't select with the square shape in edit mode. I have no other choice than pressing C. Here is my blender file in edit mode and you will see what is wrong.
If you click and hold the select tool on your tool bar, you can change to different modes of selecting. You might have accidently changed it with the "W" hotkey on your keyboard which is the shortcut to cycle through them.
Thx! :-)