Im using avast whole time, never had problem also using it on my second notebook with no problems with skype.
(EDIT: the older one im not using it too much these days)
I tried, sent some messages and after like one minute window just disappeared, tried to turn it on again but again after few seconds just disappeared without any info.
Do you have any VPN/proxy applications installed?
Please, run the "tasklist" command, which will show which processes are running on your computer.
With this command:
tasklist > f:\Games\tasklist.txt
Im not able to create the text file with it (the folder is existing i have steam and other stuff installed there), i can maybe screenshot the Task Managers with procceses.