Go onto Amazon.co.uk, to My Account, then Manage Kindle. See what it says in there about what devices are registered to your account.
Mine lists the Kindle first, then the other devices
Nick's Kindle [email protected] Kindle Keyboard
Nick's Android Android
Nick's Kindle for PC 2 Windows PC
Nicks Kindle for PC Windows PC
Not sure why I have two Kindle for PC but I think it's due to having had the software on an old laptop, then installing on my new laptop.
Below the list of devices is WhisperSync... make sure that says ON.
Has DH let you open your Kindle box before Xmas? Guess he has if you are now trying to sync it with Kindle for PC.
Is the Kindle connecting to your WiFi correctly? Check you can navigate KindleStore on the Kindle.
Try going on the Amazon website and downloading the book from there - it should give the option of which device to send it to. Send it to the Kindle, then see if the Kindle auto downloads it. Free kindle books
See if any of that helps to get the Kindle to sync with your existing library.