Yea thats what I thought too, I uninstalled and reinstalled and it didn't help. I also noticed that when logged in under the profile where desktop connector runs you cannot connect to anything over ssl. Page Cannot Be Found is thrown for any https site.
I'm not sure how tech savvy you are but you can secure SSL test to your mail server to see if your computer can connect to it or see if its just your browser that is having issues.
Looking at your log file the desktop connector is using a local proxy you have installed on your machine thats configured in Internet Explorer browser. Did you set this proxy up manually? Do you have a proxy? Is your proxy configured correctly to handle SSL or any traffic on porn 443?
Check all of those settings and make sure its correctly set in your browser as well under Internet Options.
Good luck