I've heard of eBay screwing around with the site and creating problems whereby you can't submit Best Offers without providing credit or debit card details, but so far I've only had one instance whereby I was forced to provide my card details before the payment was taken, and that was when I made a Best Offer for an item. I've since removed the details of that card from eBay's system and have had the card stopped and replaced with a new one, so eBay couldn't use that old card to take payment again even if they were able to find a record of the card that they used to take payment from before I even had the opportunity to contact the seller and make arrangements to collect the item and pay with cash, as per the request in the listing.
To be honest I don't trust eBay with my card details - when shopping on eBay I always pay via PayPal unless I'm buying a Collection In Person Only item and have arranged with the seller to pay in cash. That way eBay get paid via PayPal and not directly via my debit card.
If you are still experiencing problems by the time you read this response then if you haven't already done so try contacting the seller to ask him/her whether he/she would be open to the option of you collecting the vacuum in person and paying for it in cash on collection. If the seller will agree to the request then you wouldn't need your card details in order to complete the sale, although you would still need to ascertain what the cause of the problem is with regards to paying for items on eBay.
So long as you link your PayPal account to eBay you shouldn't need to give eBay your credit or debit card details, as that way they would get their money via PayPal whenever you purchased an item. If you use PayPal to purchase items on eBay it's a good idea to keep some money in the account, even if you transfer money directly to PayPal from your bank or building society, although it's worth having your credit or debit card registered on PayPal as a backup option, just in case you purchase something on eBay or on another online website where the amount you need to pay exceeds the available balance in your PayPal account. In that instance PayPal would use the money in your PayPal account and take the remainder of the money from the card that has been linked to your PayPal account.
I hope you manage to get the problem sorted and don't run into any further problems when trying to purchase items you wish to buy.
