In case this is still relevant, I had good results with this:
LCD screen cleaning wipes.
Compressed air can.
Squeezed the LCD wipes and let a drop or two fall on the trackball and pressed and rolled, until it was dry again.
Pressed the trackball and used the tip of the straw on the compressed air can to blast air all around it.
While I was at it, used the still damp LCD wipes on the screen, areas left and right of the trackball, and keyboard, and more compressed air on each row and column of the keyboard. Waited until everything looked dry and put the battery back on. And everything works.
Considering that I've been abusing this unit since 2008, I would say it is well spent maintenance (I can use the LCD wipes and compressed air on many other items).