TL;DR
I have computer running Windows 7 64bit, my ISP informed me that it might be infected with Sailty. I updated system, made sure the anti-virus is up to date, preformed scans and found nothing. It might be an error (or something else) on the ISP part, but just to be on the safe side, I'd like to make sure that my machine is not infected. Is there anything I can do to determine if my machine is infected with Sailty or not?
Long version:
My ISP kindly informed me that a computer in my local network might be infected with Sailty, because 3 days earlier they detected (and likely blocked) a connection attempt to Sailty botnet. They also temporarily blocked my internet connection.
They recommended updating JAVA, Flash, anti-virus, system and preforming scans. The ISP added Sailty botnet to their detection list on July 2015 (so I'm guessing they haven't detected anything during the last 3 months).
At the time of the supposed connection only one PC was on and had a P2P app running in the background (I'm suspecting this might had something to do with what the ISP detected).
AVG with current virus database found 3 unrelated false-positives, Malwarebytes Anti-Malware found nothing. I found a forum thread in which someone described the very same issue with the ISP. Trained technicians had a look at his Farbar Recovery Scan Tool logs and found nothing wrong, so I'm guessing that it was a false-positive (which leads me to believe it might be as well in my case). Is there some way to determine if my computer is infected with Sailty or not?
P.S. My router doesn't appear to be compromised.