I assume that if it's a new laptop it will have winXP as the operating system.
It sounds as if the uninstaller part of your programme hasn't got itself installed. Use system restore to take your computer back to the point in time before you did the first install, that will 'get rid' of the two versions of the programme for you.
Second question, turning off the computer before shutting it down properly is not a good idea, ok sometimes it's a last resort but don't make a habit of it, it can lead to corrupt files in the OS.
Steinburg Clean - have you checked it's compatability with the specs of your laptop?
Disable Norton in Device Manager to stop it running automatically, although you've needed the Internet for this problem! Sure you won't need it again????