1) Do you use Zone Alarm?
2) Do you have antivirus software on this pc?
3) Look in your event logs to see if there are any warnings or errors. To do that goto the Control Panel, select Administrative Tools, Goto the Event Viewer. Look through each log and post the Event ID and the warning or error message here.
4) When this happens again, press Ctrl+Alt+Del and choose task manager. Click the applications tab. You should see a list of apps you have running. Try killing Internet Explorer instead of shuting down your pc.