I have the same exact problem! I wanted to delete my account, just in case, but I cannot login.
I haven't used Paypal in over 10 years.
Their "service" is really not needed anymore.
I think the one you're talking about is the previous system, whereas PayPal would be the transaction processor anyway. You'd still get email (receipt?) and other bits from PayPal after the transaction was done.
Now though, the CC processing on Ebay seems to be a non-PayPal version. At least, that's what it looked like today when getting stuff. No mention of PayPal anywhere, which I was pleased with having had a very bad experience with them (PayPal) a week ago.
On the other hand, you now have to give them your SSN #.