Add the following line:
request.UseDefaultCredentials = true;
This will let the application use the credentials of the logged in user to access the site. If it's returning 403, clearly it's expecting authentication.
It's also possible that you (now?) have an authenticating proxy in between you and the remote site. In which case, try:
request.Proxy.Credentials = System.Net.CredentialCache.DefaultCredentials;
Hope this helps.