@The Iron Savior and @yetanotherjosh Thank you for the scripts!!! I ran the final version posted by @yetanotherjosh and now my Logitech Marble Trackball works perfect. The scroll wheel emulation and middle button is just what I needed to have the trackball fill my needs.
Also, a note on this... I noticed that the Logitech driver software conflicted and overrode the AHK settings and when I disabled the Logitech software, the mouse speed and acceleration defaulted to Window's settings, which don't support cursor acceleration. I found the workaround for this and wanted to share. On the Logitech configuration, if you select the 2 small buttons (numbers 3 and 4) and have "Generic Button" assigned to them, then AHK picks them up perfectly and it works just as desired while keeping the cursor speed and acceleration as configured on that software.