You didn't give any real information, other than you don't have a product key...
If you purchased through Origin, then you don't really need one as it links it to the account you purchased it on, unless you bought as a gift, in which it asks who to gift it too. Other than that, the only ways to get a Key legally is either buying one or receiving on as a gift.
If this isn't what you mean, then more info will be needed.
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I am NOT an EA employee, I am just a simple gamer like most everyone else here volunteering my help to those who may can use it .....That means I have to pay for my games just like you, lol.
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