When buying from the iTunes Store, your purchase can be interrupted if you lose your connection to the Internet during the transaction. Since the billing part of the purchase happens so quickly, your Internet connection going out usually means that you won't get to fully download the item you purchased.
When buying from the iTunes Store, an Internet connection outage can result in:
- A partial download which leaves the file unplayable
- No download at all, but a charge to your account
- A file that seems to have completely downloaded, but doesn't play
When this happens to you, it's very easy to fix. Since all of your purchases at iTunes are stored in your account, you can just use iCloud to redownload them.
If for some reason this doesn't work, report the problem to iTunes support. If you follow the standard process for this, iTunes support staff can reset your download and complete the purchase for you.
In the unlikely event that that doesn't solve the problem, try some additional support steps.