eBay do not sell anything, you purchase from sellers who list on eBay and it won't be on the account you are posting with if you bought as a guest

Did you buy a genuine battery or did you buy a death trap knock off from a random?

There is no phone number for eBay and no point ringing the number on the package

The only thing you need to do is open and follow through with a not as described dispute in it is within 30 days 

And care about who you buy from

Buying batteries from random sellers on eBay  is not only putting yourself at risk, but everyone else around you

Get help if you bought as a guest | eBay

Oh, sandy… it is disheartening … ANOTHER unbranded battery?

Even if you signed in as a guest and bought that way, you can still open a claim for an item that is faulty or not as described. I am guessing the purchase details won't be under vickthie though, but under your guest name.

As for the package 'with ebay on it', I wasn't exactly sure what you meant. Perhaps a seller printed the postage label via ebay or perhaps you saw sticky tape on the package carrying the ebay logo? I believe some time ago, ebay supplied rolls of special ebay tape etc to a lot of sellers. But the package itself won't have come from ebay, it will be from the seller.

Just having the outside wrapping is not going to prove exactly what was inside and allow you to make an ebay claim.

Your first job is to track the details of that guest account and your purchase, so you can open an ebay claim.