You can fix Error Code 53 by deleting the manifest file in the “Steamapps” folder. It will end in .acf and may look like this “appmanifest_22380.acf”.
Steam and re-launching the Steam client. If New Vegas doesn’t show up in your Library, Install again ( to the same folder ). It will now verify the existing files, which should take a minute or so, and then New Vegas will launch!