I'm not sure what exactly happened there and what steps you performed. Actually after running the remove script, you should have all Cortana files in *cortana.bak and it should be sufficient to just rename this folder by removing the ".bak" and launch it. You should then see the SearchUI.exe in Task Manager's list (Details).
If you press the Win+S key, does the search appear ? If yes, then it's possible that the search box is just hidden from the task bar: right-click on task bar - Search > ...
If that doesn't work, something failed in the middle and best would be to reinstall Cortana.