We'll address the shutdown issue later - right now let's figure out the problem with IE. Is IE the only app that doesn't open quickly? If so, please try any other browser (Firefox, Chrome, Opera, etc) and see if they open quickly. Also:
1) What is new or different since the last time everything worked properly (ie, new hw, new sw, virus, error, etc)?
2) Have you run full system scans with both your av AND with MalwareByates? If not, please to so now.