Your ability to ping an internet site proves you have a connection and internet access. If you were also able to ping a site by name (e.g.,
www.yahoo.com) it shows that DNS is working.
So (I don't know Vista so things may look a little different) go into Internet Options - Connections tab - and check your Dial-up Settings to make sure you're not using a proxy or something like that. Also check the Security tab to make sure those settings look OK.
If you have a 3rd party firewall (internet security) running, or if you have enabled Vista's outgoing protection, is it configured to allow your browser to use the internet?