How do I detect if I am part of a botnet

ashraya writes: My father (Not too computer literate) has a desktop and a laptop both running windows in his network back in Hyderabad, India. I set up a Linksys router for him to use with his broadband service. For some reason, he reset the config on the Linksys, and connected it up without Wireless security, and also with the default admin password for some time. As you would expect, both the windows computers got 'slow', and the desktop stopped connecting to internet completely for some reason. As I logged in remotely to 'fix' things — I noticed on the linksys log that the laptop was making seemingly random connections to high numbered ports on various IPs. I did a nslookup on the IPs to see that they were all either in Canada or US, with comcast and other ISP addresses.

Is that a sign that the computers were in a botnet? Are the other hosts part of the botnet too?

I have since rebuilt the windows hosts, and this connections are not happening now. I have also secured the Linksys.