You can have a PayPal account without having a credit card or bank account by purchasing what are called MoneyPaks. You buy them at brick-and-mortar stores, in addition to a service fee. You don't even need to have a PayPal account at the time of purchase, since you don't deposit the money in the MoneyPak until later.
Go to a store that sells MoneyPaks. Chains that sell them include Wal-Mart, CVS, Walgreen's, Rite Aid, Kroger and Kmart.
Pay for the MoneyPak with the amount you want to add to the PayPal account, plus a service fee, which is $4.95 maximum. You can add between $20 and $500, up to $1,100 at Wal-Mart.
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Log into PayPal and create an account, if you don't have one. Go to "My Account," "Add Funds," "Add Funds from MoneyPak."
Enter the number at the bottom of your MoneyPak ticket, or enter the activation number on your receipt if you bought it at Wal-Mart.