RFCC,
If you can ping the mailserver - and resolve its name - on isp1, but not get out to the public internet, then I suggest you contact isp1 support.
You can check if it is a DNS problem by pinging bbc directly - i.e. 212.58.224.125 - if you can ping the IP but not the name, then it's a DNS problem.
Otherwise, your network and internet connection to isp1 seems fine (you can ping the mailserver). So it looks like it could be a problem with your isp.
I assume that isp1 is a broadband connection - do you have a hardware firewall between your PC and the isp?
Obviously your dial-up connection would bypass this firewall.
Nothing puzzling if both browsers - ie and ff - are unable to access the internet over the same connection. That's what you would expect.