You need to define an EnvironmentEvents macro. See the general description on how to do this here: Customize Your Project Build Process.

And here is the code you can directly paste in the macro environment to check missing files:

Private Sub BuildEvents_OnBuildBegin(ByVal Scope As EnvDTE.vsBuildScope, ByVal Action As EnvDTE.vsBuildAction) Handles BuildEvents.OnBuildBegin
    For Each proj As Project In DTE.Solution.Projects
        For Each item As ProjectItem In proj.ProjectItems
            If (item.Kind <> "{6BB5F8EE-4483-11D3-8BCF-00C04F8EC28C}") Then ' only check physical file items
                Continue For
            End If

            For i As Integer = 1 To item.FileCount
                Dim path As String = item.FileNames(i)
                If Not System.IO.File.Exists(item.FileNames(i)) Then
                    WriteToBuildWindow("!! Missing file:" & item.FileNames(i) + " in project " + proj.Name)
                End If
            Next
        Next
    Next
End Sub

Public Sub WriteToBuildWindow(ByVal text As String)
    Dim ow As OutputWindow = DTE.Windows.Item(EnvDTE.Constants.vsWindowKindOutput).Object
    Dim build As OutputWindowPane = ow.OutputWindowPanes.Item("Build")
    build.OutputString(text & Environment.NewLine)
End Sub

It will display the "missing file" text directly in the Visual Studio "Build" output window. It should be fairly easy to understand and tune to your needs. For example, you could add errors to the error output.