This is something I really worried about when purchasing since the only way to do it was by delivery, if anything goes wrong you can't just go see the person or shop who sold it you, thankfully mine is ok sorry to hear your having problems.
@sirgelson Did you throw away the box that the Chromecast and controller came in? The only place where there's an easily identifiable serial number is on the sticker that's on the white Stadia Box which contained both pieces of hardware. It would SEEM to me that they should accept that serial number if you're returning everything.
Also, if you still have the email you got with your Stadia code, (the one that says "It's Time To Join Stadia!") there's a part in the email where they give you your serial number in a paragraph about returns. It is probably just the controller serial, but it should be enough. Here's a picture of the paragraph in that email (my serial is blurred intentionally in the picture)