My ISP suspended my IP today because they spotted spam activity from this network last night at 3 AM. I leave this computer on over night. I want to know if there a quick way to detect if this computer is the culprit?
There are a few things you can do:
A quick PARTIAL check could be to leave your computer on with web browser etc loaded on a simple page - like google, and make sure you are not using anything (like no mail checks).
Check to see the lights on your modem to see if they are flashing. Particularly if the LAN light on the port connected to your computer flashes quite a bit - and the WAN or PPP port as well.
This will tell you if traffic is leaving your computer.
(As indicated, this is a quick rough and ready check to give you confidence or confirm a suspeicion, its not meant as an alternative to BriGuys solution, and false positives and negatives are possible - for example if your machine is doing something legitimate you arn't aware of or if its scheduled only to active at certain times)