Don't use windows update if you are having trouble with it. Use the standalone fix (the ones i provided), download them and run them, tell me what they say.
After the SFC scan, do you get errors that were fixed, or no errors at all? If you get errors, you will need to restart the computer, scan again, restart after the scan, and then scan once more to ensure everything is completely fixed. I know, it is an annoying process. Restart after the 3rd scan.
I've not heard much about kaspersky, so i don't know if it conflicts with windows update or not. some antiviruses do conflict with normal operation, some don't. If you full scanned with both programs fully updated, i would think you should be virus free.
Make sure you click those links I provided and run each and every one of them. They each provide a good chance of fixing your problem, and there is no reason that they shouldn't be run.