I agree with Hannah. Having nothing in it shouldn't have ruined it and I would definitely take it back with or without receipt. It's best to have your receipt if you want your money back but if not they'll definitely give you store credit.
I wouldn't think that by turning a microwave on without anything inside would damage the microwave. It's possible something is wrong with the door. Some microwaves have built in fail safes to ensure you don't have the door propped open and it running. It's possible this was triggered and has made the microwave stop working. If it's not working, I would try to return it to Target. They have a pretty solid return policy. Just make sure you take your receipt!
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