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If it needs a PSU to push more power through it than what the OP is using then there's something wrong with it.Are they trying to fob him off though? It doesn't boot for him, and I'm guessing unless they're lying it does boot for them.
how long have you had it?
I did get the card checked on a friends machine with a Haswell i5 who uses a 980ti on a Corsair RM650w and it also failed to boot with exactly the same symptoms.
Can you borrow a different card to test your system?
This is why I stick to more reputable companies with no quibble rma's.
These mickey mouse budget gpu manu's rma is flakey.