Jon Skeet is on the case - WebClient.DownloadString is easy as (eating) pie:
var client = new WebClient();
MessageBox.Show(client.DownloadString("http://localhost:28642/api/departments/Count"));
IOW, the code I originally showed is definitely overkill for retrieving a scalar value.
UPDATE
Better yet:
private void buttonGetDeptCount2_Click(object sender, EventArgs e)
{
MessageBox.Show(GetScalarVal("http://localhost:28642/api/departments/Count"));
}
private string GetScalarVal(string uri)
{
var client = new WebClient();
return client.DownloadString(uri);
}