Dim path as String = "c:\temp\temp.exe"  ' Полный путь
Dim exeShnik as String = "temp.exe"  ' Ваш exeШник
Dim processName as String = GetFileNameWithoutExtension(exeShnik)
Dim myProcess as Process
for each myProcess in Process.GetProcessesByName(processName)
   If myProcess.MainModule.FileName = path then
        MsgBox("Есть такой")
        Exit For
   End If
next

Dim currentProcess As Diagnostics.Process = Diagnostics.Process.GetCurrentProcess
Dim moduleName As String = currentProcess.MainModule.ModuleName
Dim processName As String = System.IO.Path.GetFileNameWithoutExtension(moduleName)

Dim myProcess As Process
If Process.GetProcessesByName(processName).Length >  1  Then
    MsgBox("А я уже запущена")
    Application.Exit()
End If

Dim currentProcess As Diagnostics.Process = Diagnostics.Process.GetCurrentProcess
Dim moduleName As String = currentProcess.MainModule.ModuleName
Dim path As String = Diagnostics.Process.GetCurrentProcess.MainModule.FileName
Dim processName As String = System.IO.Path.GetFileNameWithoutExtension(moduleName)

Dim myProcess As Process
For Each myProcess In Process.GetProcessesByName(processName)
    If myProcess.MainModule.FileName = path Then
        If myProcess.Id <> currentProcess.Id Then
            MsgBox("А я уже запущена")
            Application.Exit()
        End If
    End If
Next