There are three ways to connect to the Internet: regular dial-up, which is slow, broadband (cable), which is very fast, and DSL, about which I know nothing except that it uses a phone line in some way and is also fast.

So, (1) Which way are you using to connect?
and (2) Who is your Internet Provider?

Internet Explorer and Firefox are browsers (a sort of window you look through to view the Internew), not providers. There are loads of providers: AOL, MSN, NetZero, PeoplePC, Cox Cable, JUNO, and so on. If you can contact your provider, they might be able to tell you what to do to solve your problem. Firefox, or the company that maintains it, Mozilla.com, also might be able to help you. The problem should be solvable. I think FF is a great browser.

I don't quite understand your dilemma, though, especially the bit about Firefox stating it is from another computer. Can you tell us exactly where (in what sort of box, etc.) and in what words Firefox is telling you this? Or is it really Internet Explorer that is giving you a hard time?
To find out, look at the upper left corner of the browser where you get this message, and you will see either a blue "e" for I.E., or the icon of a blue globe with an orange fox wrapped around it for Firefox.

I don't see how there can be another computer involved unless your computer is on a network with other computers.

You said, "so further checking I find that Firefox states its from another computer." What was it you did to check this? It is Internet Explorer, not Firefox, that has the Tools>InternetOptions>Connections menu with that "Never dial a connection" thing that you mention, so I think there may be some confusion as to which browser you are looking at.

We used to have a dial-up connection, but switched to broadband a few years ago and switched from I.E. to Firefox after that, so my mind is a bit fuzzy about dial-up. On the other hand, your statement that your computer is set at "Never dial a connection" makes me think maybe you have broadband. There would be no need to dial because you would always be online so long as your computer is on.

I'm sorry I can't be more specific to help you, but if you can answer the questions I have asked here, it may give someone who knows more than me a lead to tell you what to do.