PayPal have more or less admitted that there are problems for some users logging in to complete payments, either direct or using the eBay flow. There are many threads on the eBay forums about this problem, for example;
(Remember, PayPal, Skype and eBay are the same beast.)
It is faintly amusing that every time somebody reports the problem, PayPal ask for browser, operating system, screenshots, etc. – delaying tactics, I’m sure that they have identified a cause already.
There is a history of similar problems going back to April, and Grace’s theory is that it is a result of the changes to the eBay look-and-feel at around this time.
But I have worked out a solution – a bit sneaky, but works for both eBay and PayPal – use the mobile sites from your usual browser.
To login, bid and pay from eBay: eBay mobile site – this works for UK accounts too.
To pay for an item through PayPal: PayPal mobile site – you will need to know the item number if paying for an eBay item, or the email address of the recipient for another payment. Again, this works OK for UK accounts.