Greetings @quasikwazii
and welcome to this Apple (user-to-user) Community!
Re: "Missing purchased audiobooks : My audiobooks purchased in 2010 are missing from iTunes. They are not in "purchased", not available for download, not hidden".
Here is Apple Support's article on how to redownload books and audiobooks"
You can scroll to "How to redownload audiobooks on iTunes for Windows"
just in case there are some helpful tips:
and also, you can: "Learn what to do if you can't redownload an item or if you don't see the item in your purchases." If there's an issue when you redownload apps, movies, or other content from Apple - Apple Support
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Re: "I have followed all the steps on the Help pages.
The computer is authorised for downloads."
Apple has always advised us to download and save copies of our purchases for safe-keeping ... you may want to check whether or not you have a copy of each purchase backed up safely. Eg: 16 years is a long time ago ... perhaps you have an older computer with audiobook copies, or an external hard drive with back-ups of older files, or perhaps you bought them on an older Apple Account, or family purchases, for they may not appear in your current purchase history if so.
Eg: Apple support's online article (link below):
About purchasing films, TV shows, music, books and ringtones from Apple
Eg: says:
"Any digital media you buy from Apple can be permanently downloaded on to an iPhone, iPad, Mac, or Windows PC.
Content you purchase from Apple will generally remain available for you to redownload or otherwise access from Apple. Although it is unlikely, content may be removed from Apple Media Services and become unavailable for further download or access (for instance, because Apple loses its right from the content provider to make it available).
"To ensure your ability to continue enjoying your films, TV shows, music, books and ringtones, download all purchased content to a compatible device in your possession.
You can permanently download purchased content to your iPhone, iPad, Mac or Windows PC. Once downloaded, you can access content without an internet connection, and Apple can’t remove it from your device."
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Re: "I still have the receipts".
You can check the receipts to see whether payment went to Apple, or to a bookseller, distributor, or vendor you could contact.
Items not listed in your payment history may have been purchased directly from the distributor of the audiobooks, with Apple acting much like a bank does to assist with purchases. In that case you could check on availability for re-download via the contact details listed on the receipt.
All the best :-)