I'm sorry you would feel bad asking for the receipt, or a gift receipt, from the person who gave this item to you.
Personally, if someone I gave a gift to were to tell me that something went wrong with my gift and they needed the receipt to exchange it for one that works, I would locate the receipt immediately and get it to them. I would hope that someone who gave me such a wonderful gift would be equally understanding and get me the receipt if needed.
Best Buy and pretty much ALL stores would deny this return without a receipt, because they have no proof that it was purchased from them. Let's say for instance it was actually purchased from a competitor, why would they accept a return on it? Oftentimes they are losing money making returns, if there isn't proof it came from them, why should a company accept the return?
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Before posting I try to research everything first or use my own experiences. I do not now nor have I ever worked for Best Buy. I work for the competition.
If you respond to a post of mine, I will read it. I may or may not post in the thread again, but rest assured I will read your response