I would check the size of your gizmo.  One of my students had the same problem and it turned out that the gizmo was far too big to see on the screen.   To make sure, go back to the preferences menu and put the sizes to what you see below.  Other than that, the "X" hotkey turns the gizmo on and off but that does not sound like your problem.

Hello!

I had same problem. Has decided the following way.
For 3ds Max 8 if axes XYZ gizmo were gone and them it is not possible to include a key "X" on the keyboard:
Open with help WordPad file 3dsmax.ini in the main directory 3ds Max.
C:/Program Files/Autodesk/3dsMax8/3dsmax.ini
Change value of parameter
TransformGizmoRestoreAxis = 1
On
TransformGizmoRestoreAxis = 0
After that axes "Gizmo" will appear back and button " X " will earn.

P.S. Forgive for my English.