Did you run the uninstaller? I find it odd that bittorrent's GUI would uninstall, but leave the core program running.
My guess is that the core program was probably just updating the servers that direct traffic to say where you were and what files you were sharing. And you can not get hackers in to your system just by running P2P software. The people who designed the internet were smarter than that.
The issue is when you want users to log in to your system remotely, and you want to keep out people who aren't legitimate. For instance, at work there's a way for people to submit code and access files from home. It's through that same pathway that a hacker might try to breakthrough and access files and submit code, etc. But the hacker can never do more than a legitimate user could.
Another example: windows has something called remote desktop. It basically lets you connect to another windows computer through the internet. I have a small server farm I'm setting up, and I can turn on any of the computers, and log in to them, and run them just like I was there, on my desktop, even though my actual computers are in another room. In theory if someone were to figure out my password (brute forcing it or using a dictionary attack wouldn't work. Most passwords are found either because people write them down, throw them away, and the hacker digs through the corporate garbage, or the hacker is the one who set up the network and knows some back door password, or something like that), and they were on my LAN, they could gain control of these computers like they were sitting down in front of them.
However, my router does not allow incoming traffic from the internet to access the ports you need for remote desktop. So it is impossible for anyone to get at these computers from the internet unless they can first hack my router. But my router specifically does not allow incoming traffic from the internet to access its login page. So it's physically impossible for someone to hack my computers through the internet.
However, my router is wireless, and I haven't set up a password for it (because I'm lazy), so in theory someone could get within 50 feet of my house, use my wireless router to connect to my Lan, and then somehow figure out my password, and log in to these spare computers. But that's the only physically possible way, because I'm specifically not allowing incomming traffic from the internet to access the stuff it needs to hack my computer.
If you just have a vanilla install of XP, fresh out of the box, with no fixes, and hook it up to the internet, you won't get hacked. Hacking can only occur if you, the user, install or run an executable on your computer. Either something involving outlook or word macros, an installation package, batch files, etc. etc. Or if you the user specifically set your computer up to be accessible from the internet. And even then someone has to figure out your password, and if you make it 8 letters or longer, and mix lower and upper case with some numbers, it becomes impossible*.
* at the present time. Most systems rely on a mathematical fact that it's hard to factor large numbers. If that ever becomes easy, pretty much all existing protection schemes become trivial to break. Of course, you still have to have your computer set up for remote access.
