First the ISA modem.
Alot of Internal modems do not work with Linux, this is because they contain the very minimum of components and get Microsoft to do most of the work. Therefore you are generally much better off with an external modem (all the required parts are there).
Next the External modem.
Connect to your ISP with the modem and then try pinging 188.8.131.52 (www.google.com
This will tell you if you can connect to the internet. I would imagine you are having a problem with DNS. The internet is afterall a collection of servers on a (very) large network. As such you need to know how to find the specific machines that you want to speak to.
If you're using a dial-up connection to an ISP you need to add their DNS server to your /etc/resolv.conf file.
You should be able to find your ISP's DNS server address from their website. EG. for zoom.co.uk there should be the following entry: