From the stock code (.NET starter projects for API) they use exception type to make this distinction. It looks like we're assuming that if we get a coherent Soap response from the server that is nonetheless an error, it is probably a login problem. By extension, other types of errors indicate we were not able to get the server to acknowledge our attempt. The code I use is below, the relevant bit in blue.

        Public Function loginSalesForceServer(ByVal UserName As String, ByVal Password As String) As Boolean
        Dim loginRes As sforce.LoginResult

        Dim un As String = UserName
        If un.Length = 0 Then
            Return False
        End If

        Dim pw As String = Password
        If pw.Length = 0 Then
            Return False
        End If

        '/*
        '* Create the sfbinding to the sforce servics
        '*/
        sfbinding = New sforce.SforceService

        '// Time out after a minute
        sfbinding.Timeout = 60000

        Try
            loginRes = sfbinding.login(un, pw)
        Catch e As System.Web.Services.Protocols.SoapException
            '// This is likley to be caused by bad username or password
            Return False
        Catch ex As System.Exception
            '// This is something else, probably comminication
            Return False
        End Try

        sfSessionID = loginRes.sessionId
        sfServerURL = loginRes.serverUrl

        '//Change the sfbinding to the new endpoint
        sfbinding.Url = loginRes.serverUrl

        '//Create a new session header object and set the session id to that returned by the login
        sfbinding.SessionHeaderValue = New sforce.SessionHeader
        sfbinding.SessionHeaderValue.sessionId = loginRes.sessionId

        prvSalesForceLoginState = "Logged In"

        Return True
    End Function