Mysterious network activity.

I have a broadband connection through an ethernet cable to my PC running WinME. The LEDs on my network card are in view, so I know that usually the green one is constantly on, and the amber one blinks at a sedate rate. When I am actually uploading or downloading data, that blink rate increases. Sometimes, even if my email client (Outlook Express6) and browser (Firefox 2.0.0.20) are NOT open, the amber light blinks furiously - suggesting to me that data transfer is occurring. But WHAT and WHERE TO or WHERE FROM is a mystery to me. My obsolete but age-compatible firewall, Sygate Personal Firewall has entries in its traffic log that are 5 minutes behind current time, so can't tell me what is happening NOW. It however does seem to store about 24hrs worth of data. (How) can I find out what the 'unauthorised' or mystery internet traffic is about ?