This is VB 2005 though. So you really want to use the System.Diagnostics.Process namespace.
Private Sub LaunchGame(ByVal GameName As String)
   Dim myProcess As Process = New Process
   AddHandler myProcess.Exited, AddressOf MameExited
   myProcess.StartInfo.WorkingDirectory = "E:\Emulators\Mame"
   myProcess.StartInfo.FileName = "E:\Emulators\Mame\Mame.exe"
   myProcess.StartInfo.Arguments = GameName
   myProcess.StartInfo.CreateNoWindow = True
   myProcess.StartInfo.WindowStyle = ProcessWindowStyle.Hidden
   myProcess.EnableRaisingEvents = True
   myProcess.Start()
End Sub
Private Sub MameExited(ByVal sender As Object, ByVal e As System.EventArgs)
   MessageBox.Show("Mame exited!")
End Sub