If the product key was for OEM Windows 7 Home Premium 64 bit, meaning if all that is spelled out above the product key on the sticker, then it should have activated with the disc you have shown us.
It is possible (even if unlikely) that you mis-typed the key when you attempted to activate. An 8 instead of a B, or an O instead of a 0, an H instead of a K, etc. I know that's a long shot, but I had to include it on the off chance.
I can positively say that I have successfully activated OEM installer versions of Windows (up through and including several Windows 7 installations) with OEM product keys. Most of them were fresh installs of Windows using the OEM keys on the bottom of laptops, but there were also a mess of desktops in there. In the heady days of Windows XP, I was recycling those keys of dead machines and re-using them. sigh
From everything you describe; the seller, the disc, the product key sticker... it should still activate. You may have to use the phone activation system however. I had to recently, when I used the OEM key from a dead Toshiba, to install Windows 7 on a desktop.
- Click Start.
- Right Click Computer
- Choose Properties
- At the bottom, choose Activate Windows Now
- From the Wizard Popup, choose Use the automated phone system to activate.
- Follow the prompts, answer the questions, call the number they give you, jump through the hoops.
From the Microsoft Article here. I believe this will solve your issue.
At the end, again, providing the OEM key has never been used before, it should activate.
If it does not, then your next call should be to Amazon to exchange this purchase for another of the same. Yes, I would take this to be some kind of fluke. I would describe the issue to them, and rather than demanding a refund I would just ask them to provide another of the same. This will make them more likely to actually just ship it out. They might give you some flak about it being software, etc... just be clear and sure about the fact that Microsoft is repeatedly telling you that it isn't a valid product key.
From what I'm reading, there are plenty of people installing OEM versions of Windows 7 on Macs via Bootcamp... it actually seems quite popular. Most of their posted issues are with attempting to use the same copy for the installation AND a VM installation, and having to activate it twice in that instance. This is NOT the issue you are facing, but I'm including that information because they have no issues with an OEM copy of Windows 7 for the first activation. They run into issues when attempting to install it again, in a VM (or Parallels) and try to activate it a second time on what may (and can) appear to be different hardware. Their first activation (just like yours) works like a charm.
So try the Automated Phone Activation System.