>>>I have been getting messages from Norton saying my computer is dreadfully infected and I should download Norton to rectify this problem
I'm prepared to bet that you
haven't been getting messages from Norton. (Why would you, if you're using Kaspersky?).
It matters not whether you're using Kaspersky, Norton, MacAfee, AVG, Avast, Comodo or anything else. None of them will block all MALWARE. That's almost certainly what you've got on your computer and accepting the offer to download something from Norton will, instead, download and install something extremely nasty, such as Cryptolocker:
http://www.bbc.co.uk/news/technology-25506020
So you need to get rid of that malware. Download, install and run the free version of Malwarebytes:
https://www.malwarebytes.org/free/
Points to note:
1. When installing, take care to deselect the option to install free trial of the 'PRO' version ;
2. When running it, use the 'Quick scan' option ;
3. Don't be surprised when that 'quick' scan takes over half an hour to finish ;
4. When it does so, click the button to view the results, ensure that there's a tick alongside everything listed and then click the button to delete what's been found.