I don't think you can use PayPal to make payments until provide a credit card or bank account. Their policy is pretty clear - just not well disseminated. It would be nice if they made this very clear before you signed up. Their policy statement:
For security reasons, you will not be able to use your PayPal account to send money until you have added a credit card. Once you have added a credit card to your PayPal account, your Sending Limit will be increased to $2,000. This limit applies to all payments regardless of how the payment is funded or to whom the payment is sent. Once you send payments totaling $2,000, you will no longer be able to send payments until you lift your Sending Limit by becoming a Verified Member of PayPal.