Just a question about RATs

The past two days i've had trouble because some assholes were ddossing me. But yesterday i got hacked and after running malwarebytes/spybot search and destroy/ avast. All 3 in safe mode, i picked up a keylogger.

There is absolutely no way i've dl'd a keylogger, i havent dl'd anything the past few days. And after all that, i started to investigate and i found out i had installed bitttorent recently. And i knew something was up because i never had bittorrent.

I looked at my file history and the evidence shows that they remotely controlled my PC and the keylogger was downloaded manually from my computer, thus bypassing my antivirus. I found the installation files, the serial key and crack, installation notes of the keylogger.(I will not name the keylogger for user safety)

How could this have happened? I remember early this month i restored my PC to factory settings to run skyrim more smoothly, but apparently just from knowing my IP these hackers were able remotely access my computer. This led me to think, this might have been a RAT, but.....just as i know i did not download a keylogger, theres no way i downloaded a RAT either. I know all about Java drivebys and i set java to update manually only.

My brother's laptop was also hit with the same exact results. Hackers remotely access his PC and download the keylogger from the PC itself via bittorent.

So far the measures i've taken was disable all incoming connections, shut off remote assistance(stupid windows has it on default), fired up firewall on max settings.

I just need some expert help on this, as im just confused. i know what happened, but what i dont know is HOW. I dont visit suspicious sites, but these hackers somehow managed to do everything via my IP alone.