Kaspersky Products Remover is a portable tool which can completely uninstall almost any recent Kaspersky application. You should always use the official uninstaller first, via Control Panel's "Programs and Features" applet, but if that's not working then Kaspersky Lab Products Remover is a simple alternative.
The program doesn't require any special preparation, booting into Safe Mode or anything else. Just unzip it and you're ready to go.
You're asked to agree to the program licence, but after that all you have to do is to enter a code (a simple CAPTCHA to prevent the Remover being used automatically), select your product if it's not already been detected, and click Remove.
The Product Remover should then properly uninstall your Kaspersky software, but the files may still be visible until you reboot.
If you have several Kaspersky products then you'll need to run the Remover for each one.
Kaspersky Products Remover creates a log file in the same folder as itself, recording the details of the uninstall. If it doesn't work as you expect then this might offer some clues.