From what you said clearly the original file is still on the old computer. You need to move things from there properly or if it is too late to do that then hopefully you can download it again.
Downloading (using iOS or computer) past purchases from the App Store, iBookstore, and iTunes Store - http://support.apple.com/kb/ht2519 - enabled with iTunes 10.3 and newer; not all media formats are available in all countries (see: iTunes in the Cloud, iTunes Match, and iTunes Radio availability by country - http://support.apple.com/kb/HT5085); apps, books (not audiobooks), music, t.v. shows, and movies (some - not all studios have permitted this). Downloading previously purchased movies and TV shows requires iTunes 10.6 or later. Discontinued items not available. For items not included in the iCloud list (e.g., ringtones, audiobooks, alert tones), or locations or computer systems where iCloud is not (yet?) available, you only get one download per fee paid. Apple recommends, "... back up your iTunes library. " (http://support.apple.com/kb/ht2519).