There are multiple ways to fix this.

First, you could use the official message loop from Using Messages and Message Queues, so replace your while(TRUE) ... by this:

BOOL bRet;
while ((bRet = GetMessage(&msg, NULL, 0, 0)) != 0)
{
    if (bRet == -1)
    {
        // handle the error and possibly exit
        break;
    }
    else
    {
        TranslateMessage(&msg);
        DispatchMessage(&msg);
        // don't put Render() here
    }
}

And then do your render loop in WM_PAINT. This is what you wanted to do but one important detail is as doc says:

Return value An application returns zero if it processes this message.

So replace your WM_PAINT handling by this:

case WM_PAINT:
  Render();
  return 0; // we handle it

What it means to Windows is in fact you never validate your update region so Windows keeps sending the WM_PAINT message.

Another solution (more common in DirectX gaming loops) is to keep Render in your current message loop and handle WM_PAINT just validating the region, like this, so Windows won't send it forever:

case WM_PAINT:
{
  PAINTSTRUCT ps;
  HDC hdc = BeginPaint(hWnd, &ps);
  EndPaint(hWnd, &ps);
}
return 0;

And change your current Input::GetKeyRaw(Key key) implementation because it runs another message loop which causes weird things. Move WM_KEYDOWN handling in the main loop, and simply store the keyboard state somewhere so you can use it in Render().