I had to ask.
I'd recommend a [link|http://z.iwethey.org/forums/render/content/show?contentid=195304|hardware firewall]. It would save you a lot of grief in situations like this.
I don't know if you're infected yet. You might be getting hammered by folks looking to make your machine a zombie, but might not actually be infected yet. But it's hard to know. It doesn't sound right that you're sending out packets when you shouldn't be, but it might be something in Winders doing that.
I'd be suspicious about the system having trouble finding the modem early on. That might indicate that something is amiss.
Until you get a hardware firewall, I would suggest wiping your system again (using a known-good FDISK/format program) and getting a copy of MEPIS or some similar Linux live CD (from a friend perhaps?). Use it to download everything you need for Windows. Disconnect from the network, do a fresh install, and install all the patches and protections before you connect to the network.
[edit:] It's worse on the server side of Windows. [link|http://www.theregister.co.uk/2005/03/18/windows_server_firewall/|TheReg]. [/edit]
[edit2:] I finally remembered that you're on dial-up. It's difficult to use a hardware firewall with dial-up unless you get a box that works with an external modem. I have an old [link|http://froogle.google.com/froogle?q=DI-704p&btnG=Search+Froogle&scoring=p|DI-704p] (the brown model) that worked well for me for that purpose when coupled with an external USR V.90 voice faxmodem. I see the DI-704p can be had for $20 at various stores, and as little as about $3 on eBay (but be careful - it looks like the newer silver models don't have a serial connection). An external V.90 modem can be had for $10-$20 or less on eBay. You'd need a serial cable between the modem and the DI-704p, and a CAT-5 cable between your PC and the DI-704P. More on the wiring is [link|http://z.iwethey.org/forums/render/content/show?contentid=50525|here].
If you're interested, I might be prepared to part with my stuff. :-) [/edit2]
HTH. Luck!
Cheers,
Scott.