There is a winsock repair program that I've used in the past, with maybe a 75% success rate....but I can't remember the name of it...
Ok, just googled it and came up with this one HERE
(which I've used maybe once or twice, can't remember if it worked or not, been a few years!). Read everything and follow the instrutcions to the Tee!
However, since you said that you just now got broadband, I'd call up your ISP and make sure that they've actually activated your account, better be safe than sorry. Now, they should also have techs that can help you on the phone.
I'd have to agree with Sterling 14 about the issue being the comptuer (Windows). If it's not the Ethernet port itself, then it's most likely windows (winsock). There's some other things, like making sure that your onboard lan it enabled in the BIOS, but I don't think that's it if it recognizes that there's no cable plugged in.
Try the Winsock repair program. Do a search for "Winsock repair" and "Winsock repair programs" (without the quotes) and do some reading on it. A winsock file gets messed up when things are removed incorrectly (programs that have been removed either manually like deleting the file instead of uninstalling the program, or certain spyware removal programs can remove parts of a program).
Hopefully, repairing your winsock file will fix it. If not, then you may have to reinstall Windows XP, which really isn't all that bad, although it's somewhat time consuming. I was hoping that this would be an easy fix and not be a "sorry, you've got to reinstall windows"....
Hope this helps!