How terminate a task with status = 'Not Responding'
I use the next code

Option Explicit
Private Declare Function WaitForSingleObject Lib "kernel32" _
(ByVal hHandle As Long, _
ByVal dwMilliseconds As Long) As Long

Private Declare Function FindWindow Lib "user32" _
Alias "FindWindowA" _
(ByVal lpClassName As String, _
ByVal lpWindowName As String) As Long

Private Declare Function PostMessage Lib "user32" _
Alias "PostMessageA" _
(ByVal hwnd As Long, _
ByVal wMsg As Long, _
ByVal wParam As Long, _
ByVal lParam As Long) As Long

Private Declare Function IsWindow Lib "user32" _
(ByVal hwnd As Long) As Long

Private Declare Function OpenProcess Lib "kernel32" _
(ByVal dwDesiredAccess As Long, _
ByVal bInheritHandle As Long, _
ByVal dwProcessId As Long) As Long

Private Declare Function GetWindowThreadProcessId Lib "user32" _
(ByVal hwnd As Long, _
lpdwProcessId As Long) As Long

'Constants that are used by the API
Const WM_CLOSE = &H10
Const INFINITE = &HFFFFFFFF
Const SYNCHRONIZE = &H100000
Private Sub Form_Load()
Dim hWindow As Long
Dim hThread As Long
Dim hProcess As Long
Dim lProcessId As Long
Dim lngResult As Long
Dim lngReturnValue As Long
Dim RetVal
On Local Error GoTo errhandler
hWindow = FindWindow(vbNullString, "DDS Browser")
hThread = GetWindowThreadProcessId(hWindow, lProcessId)
hProcess = OpenProcess(SYNCHRONIZE, 0&, lProcessId)
lngReturnValue = PostMessage(hWindow, WM_CLOSE, 0&, 0&)
lngResult = WaitForSingleObject(hProcess, INFINITE)
'Does the handle still exist?
DoEvents
hWindow = FindWindow(vbNullString, "DDS Browser")
If IsWindow(hWindow) = 1 Then
'The handle still exists. Use the TerminateProcess function
'to close all related processes to this handle. See the
'article for more information.
MsgBox "Handle still exists."
Else
hWindow = FindWindow(vbNullString, "Program Error")
hThread = GetWindowThreadProcessId(hWindow, lProcessId)
hProcess = OpenProcess(SYNCHRONIZE, 0&, lProcessId)
lngReturnValue = PostMessage(hWindow, WM_CLOSE, 0&, 0&)
lngResult = WaitForSingleObject(hProcess, INFINITE)
RetVal = Shell("SISme.exe", vbNormalNoFocus)
'Handle does not exist.
'MsgBox "All Program Instances Closed."
End If
On Local Error GoTo 0
Exit Sub
errhandler:
MsgBox Err.Number & vbCr & Err.Description
Err = 0
End Sub