Sounds like your customer actually paid using the "Offline Credit Card" module, and not with PayPal at all.
If you don't have a credit card merchant account with your bank, you'll need to "Remove" that offline module because you can't use it. Any transactions made using that module WILL NEVER CHARGE A CARD.
Or, if your customer did pay with PayPal, then perhaps you've configured your PayPal settings in your store incorrectly, perhaps sending the money to a completely different email address.
Have YOU actually done a real PayPal transaction on your store and seen the money go through? If not, then you owe it to yourself to actually test your store completely before opening to customers.
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