Oh, wow.
You are the first one I've seen who has [nearly] the same problem I do!!!
My Logitech Cordless [USB] trackball worked for a little while - but not since day of install, almost 2 weeks ago.
I seriously hope you get some more fix-it replies - the one I got was similiar to yours - with the proviso I not use it if I never used a console before [I just INSTALLED Linux, so, DUH!!!]
I installed Mandrake 7.0, but am also going into a KDE/X-windows desktop [whatever the hell that means...] Anyway, I am able to [clumsily] navigate around, my desktops appear to be more stable than yours.
I have the Trackball on a PS/2 connection [after two hours trying everything I own - WIndows isn't recognizing any serial devices tonight for some reason!].
How is your Logitech device connected? Is it a cordless thing?
{No joy on Logitech site, but I did print off @dozen or more pages of stuff that's helped me stabilise my Trackman Marble FX in Win98SE}.
I hope to look over your shoulder at further replies to your post, if you don't mind...