Recently I am experiencing slowdown and difficulty shutting down and startup computer?

If Webroot isn't detecting anything but you still suspect an infection, you can contact our support to double-check at no charge:
http://www.webroot.com/us/en/support/contact
 
Have you installed anything new on the computer lately?  If a new application that isn't in our database is detected, Webroot starts monitoring it, which can slow things down a bit.