Hi Zmoke!
First, make sure you are running the Epic launcher as admin. According to your latest logs, the process is not elevated:
[2015.11.30-16.30.32:687][ 0]LogInit: WinPlatform: User is admin: true
[2015.11.30-16.30.32:688][ 0]LogInit: WinPlatform: Process ran as admin: false
Right click on the Epic launcher and select “Run as Administrator”.
Second, can you check your proxy settings for me? Click Start → Control Panel → Network and Internet → Internet Options → Connections → LAN settings. What, if anything, is checked there?