pinging a name in cmd.exe (it's not DOS) uses the same mechanism to resolve the DNS name to an IP address as looking up a website in any web browser. Thus, if one doesn't work the other wont.
What you can try and do is ping an IP address as this doesn't require DNS name resolution.
Try pinging 188.8.131.52 which is one of Google's DNS servers. If you do not get a response then your wireless access point does not have a route to the internet