OK Ali1, I think that I understand now

1. If your phone line is connected to your modem, and your PC is powered up............I mean booted up NOT just "connected to the electricity supply". It is possible that a virus or other malware that is running on your machine could connect to the internet and spread itself.

2. If it is a RAT (remote access trojan) then the bad guy could upload more bad stuff to your machine, or do most whatever he wants?
Remember that there is stuff out there that will silence the modem, so you won't hear it, so unless you have an external modem and notice the flashing lights, you will not be aware.
OK, your logs and stuff might tell you what has happened, but that is only AFTER it has happened, and they won't tell you WHAT happened?

3. This is how a lot of "dialers" work?......sit there monitoring activity, if you have been inactive for a while they call a very expensive connection, and you see it next month when you get the phone bill/ISP bill. So you had better believe it

4. I am not an expert in this area, but I would have thought that there is sufficient information in your browser and mailing system to identify and connect to your ISP? The only way to avoid this would be to recreate the link for each session and delete it afterwards, and I am sure that you do not do that

5. Just have a look in your browser and mail system setup utilities, and I think that you will see what I mean............you have told them about your ISP?.............and they don't need an ISP........if your telephone is connected they can talk "direct" so to speak?

You need a good firewall that requires you to verify OUTGOING connections.

I agree that you cannot be attacked down your phone line from the outside, if you are not connected to the net..............it is the OUTWARDS connections you need to worry about.

Cheers