Had a very similar problem with one particular site that I used to get access to regularly. I could get it on a dial up modem but not my broadband at work.
The answer was to obtain the alternate DNS server address from our provider (Pipex) and enter it in the appropriate Internet protocol Settings (TCP / IP) properties > General Tab for the Broadband connection I was using.
I don`t know how or why this works but it cured the problem. BT Broadband has a freephone number for technical support. 0800 800 060. Hope this helps.