Re-activation

The way it should work is download and install Origin app, Sign in the app(make sure you use same username as when you purchased the game originally), and find the tab that says all games in the filter which should then show every game you have ever bought  from Origin on.  Once it shows all the games you have bought from origin, you will need to click on the game and choose install, which will make it dl and install the game.  If you happen to have the game still on the old HD and have access to it(installed a second or something or in a hotport) then you can start the dl wait a few min, pause it, then copy all the files from the old hd to the location of the new install, and then restart the dl...it will pause a bit and then finish up the install without having to dl most of the game.  But even if you can't copy it, the Origin app will just dl the game and install it.  As long as EA/Origin exist all your purchased games should be around and available to install on all future computers you own.