You can also go to the auction, which is still running with one last offering unsold - once there, you can click on where it says "29 sold" and it will give you a page showing the 29 completed auctions, with the bidders' names in
ebay code.
But if you are signed in to
ebay, your individual purchase, the only one on the 24th of June, will show YOUR
ebay ID (to the rest of us, it will be in code like the others).
And that shows me and the rest of us that you did complete the transaction, because the buyer on June 24th has an
ebay feedback of just one, and you did say you were new to
ebay.
I once had a seller who insisted that I had not paid him, and for some bizarre reason
ebay couldn't convince the seller that I paid (or didn't care), but luckily I had a fifteen year spotless record and scans from the transaction so eventually it got sorted out, but for a long time the seller insisted that I was trying to scam him.
Your case seems like a no-brainer, but the eBay/PayPal system works in mysterious ways sometimes. Don't give up.
One last thing to check though - did you pay with PayPal and use the same ID that shows as the buyer, no second account?
PS: One more possibility - check your
ebay purchase history as Battlestamps has suggested, and look carefully to see if it shows that the purchase is marked "Paid" and not "Pending". There could be something incomplete in your PayPal registration, if you are using PayPal.