Thank you very much for your comment and time helping me. I already checked that I'm not using any port blocker or any weird software. I really think that it's an issue that remained due to the kaspersky settings, and even though I uninstalled Kaspersky completely, it didn't work for me.
I also checked that the entire BitComet software doesn't have internet. It doesn't even work trying to download any file coming from a normal URL.
Then I remembered that installed a software called System Mechanics Pro (symilar to AVG Tuneup Utilities) which had a firewall even though I chose not to install it, so I tried installing it again and checf if it was blocking it still somehow, with no luck.
Also, I tried removing ALL KIS files using a software directly from their website: http://support.kaspersky.com/common/service.aspx?el=1464#block1
Also, I ran CCleaner as suggested, with also no luck.
Even with antivirus and a disabled Firewall, I can't seem to make it work. It's really weird. But I really appreciate the help. I'm soon going to change to Windows 10 wiping all data, and I hope it would work from there.