Many programs are designed to hide the cursor when entering full screen mode to give you a better multimedia experience. IE is a primary exception because they assume you'll still have use for the mouse, not be using it solely for multimedia content.
However, moving the mouse is usually supposed to display the cursor again, for a limited time. If that's not happening I would suspect a problem with the mouse driver and attempt to download the latest version from Logitech. Also, if you are using custom cursors, try disabling them and using the defaults temporarily.
One other thought is to disconnect the trackball and uninstall the Logitech software, reboot, and see if the same issue occurs while just using the mousepad. If so, it's likely a conflict between the two devices.
I recently bought an HP dv6000 laptop from a big box store. 1 gig RAM, dual processor, nvidia graphics card. Vista home premium was preinstalled. I am using both the built in mousepad and a Logitech trackball. My problem occurs when I use a program that runs in full screen, such as a Windows slide show and a train simulator, the mouse pointer disappears. The mouse is still working, because when I run over a radio button it reacts. When I run IE, windows explorer, go to control panel, or run a program that isnt full screen everything works fine. Any ideas what I can do to fix this problem.