Most jurisdictions won't begin accruing the statute of limitations on the date that property was stolen -- that wouldn't make any sense, because in most cases, the true owner wouldn't know who to file suit against.
Instead, jurisdictions are split as to what they do. Some jurisdictions only begin accruing time for purpose of the statute of limitations on the date that you actually found out who stole the property. Other jurisdictions will begin accruing the statute on the date that you should have, by a reasonable and diligent effort, known who committed the misappropriation.
Assuming you're not barred by the statute of limitations, I know some people have expressed sentiments to the effect that the property doesn't belong to you; it belongs to Blizzard, so you don't have standing. While that is true, you do have constructive ownership of the property, and even more significantly, you have property rights as to the access of the property.
In selling your account password and information, your friend deprived you of access to something that you rightfully had. There's a misappropriation claim in there. I don't see the fact that it was in your parents' name and not yours as a huge hurdle.