uses
  WinSvc;

function ServiceGetStatus(sMachine, sService: PChar): DWORD;
  {******************************************}
  {*** Parameters: ***}
  {*** sService: specifies the name of the service to open
  {*** sMachine: specifies the name of the target computer
  {*** ***}

  {*** Return Values: ***}
  {*** -1 = Error opening service ***}
  {*** 1 = SERVICE_STOPPED ***}
  {*** 2 = SERVICE_START_PENDING ***}
  {*** 3 = SERVICE_STOP_PENDING ***}
  {*** 4 = SERVICE_RUNNING ***}
  {*** 5 = SERVICE_CONTINUE_PENDING ***}
  {*** 6 = SERVICE_PAUSE_PENDING ***}
  {*** 7 = SERVICE_PAUSED ***}
  {******************************************}
var
  SCManHandle, SvcHandle: SC_Handle;
  SS: TServiceStatus;
  dwStat: DWORD;
begin
  dwStat := 0;
  // Open service manager handle.
  SCManHandle := OpenSCManager(sMachine, nil, SC_MANAGER_CONNECT);
  if (SCManHandle > 0) then
  begin
    SvcHandle := OpenService(SCManHandle, sService, SERVICE_QUERY_STATUS);
    // if Service installed
    if (SvcHandle > 0) then
    begin
      // SS structure holds the service status (TServiceStatus);
      if (QueryServiceStatus(SvcHandle, SS)) then
        dwStat := ss.dwCurrentState;
      CloseServiceHandle(SvcHandle);
    end;
    CloseServiceHandle(SCManHandle);
  end;
  Result := dwStat;
end;

function ServiceRunning(sMachine, sService: PChar): Boolean;
begin
  Result := SERVICE_RUNNING = ServiceGetStatus(sMachine, sService);
end;

// Check if Eventlog Service is running
procedure TForm1.Button1Click(Sender: TObject);
begin
  if ServiceRunning(nil, 'Eventlog') then
    ShowMessage('Eventlog Service Running')
  else
    ShowMessage('Eventlog Service not Running')
end;

Windows 2000 and earlier: All processes are granted the SC_MANAGER_CONNECT,
SC_MANAGER_ENUMERATE_SERVICE, and SC_MANAGER_QUERY_LOCK_STATUS access rights.

Windows XP: Only authenticated users are granted the SC_MANAGER_CONNECT,
SC_MANAGER_ENUMERATE_SERVICE,
and SC_MANAGER_QUERY_LOCK_STATUS access rights.

Do not use the service display name (as displayed in the services
control panel applet.) You must use the real service name, as
referenced in the registry under
HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services