As for online using.
"Flat" debit cards (like: Visa Electron, Maestro), that got literally flat characters on it (digits from card number, letters from card owner's name) will not allow to make any online transactions.
Cads with convex (I'm not sure about this word :P) characters issued by Visa or MasterCard (I don't know how it looks like the other companies), will more likely allow it's owner to make any online transactions. "Convex" cards should have microchip built in them. Generally they look like credit cad..
"Flat" debit cards are still in use in Poland (rather rare), so they might be in use in other countries as well.
Most common debit card presently issued in Poland is "convex".
Did PayPal provide you with a local bank account number to transfer funds (like you would make an ordinary transfer) from your normal account to your PayPal account?
In my case PayPal gave me an account number in a bank in which they have their normal account, and special id to paste in transfer title.