This is irritating, I know. My PC will try to dial out for no apparent either (and I have a DUN connection shared with Win98).
The Win98 machine isn't trying to access any net services as far as I can tell. I have disabled Dial on Demand, and will see how it goes.
What you can also try is to install ZoneAlarm.
It is free (for personal use) firewall software, that will not allow applications to access the net unless you specially tell them they can.
By installing it, you will get prompted everytime a program tries to connect. It will remember applications, so you don't have to keep telling it to let IE out on the net

One major problem I found with it (and I'll admit I didn't spend much time trying to fix it), is that your online games won't be allowed to connect to servers. And because they run full screen, you probably won't see the 'Let application X access the internet?' message. You can probably get around it by ALT-Tabbing or something, but I didn't have time to look into it.
Give it a go and see what you think. It will make more or less invulnerable against port scanning and other hacking attempts. Very important if you DSL or some other always-on connection.