Is it able to resolve the hostname to an IP when you ping/try to visit the site? If not, it may be a DNS issue. I'd recommend using
OpenDNS.
If it
is resolving the IP addres, just timing out (as it sounds like it is doing), would try running a tracert to see where exactly the connection is failing. You should flush your DNS cache, first, by typing ipconfic /flushdns in the command prompt.
You might also want to make sure there isn't an entry for the site in your hosts file (Windows\System32\drivers\etc\hosts), which can be opened with notepad.
Finally, it's possible the server isn't accepting connections from your IP address, or a range that includes your IP address. You could try contacting the bank to see if you can get through to the support for their website.