OK, I better see how it is currently installed - it sounds as though it's fully installed and running, as I wasn't quite sure if it was partially installed and lingering. I don't think the installer cleanup is a good idea unless you have to use it to fool kapersky into reinstalling...which could still be a risky task.
I would first try the reinstall/uninstall. If that doesn't work you can use the autoruns to disable the startup routines and then manually remove the program directory before rebooting however your registry will need cleaned, so if you can get Kaspersky to uninstall somehow that would be best.