It is possible that absolutely nothing is wrong with your computer, and the problem is in your Internet connection. Sites like eBay use secure connections, which are different from normal connections. If something is wrong with your computer's Internet connection, it is possible to be able to connect to some sites but not others.
It is also possible that your computer is infected with malware that tries to hijack connections to secure sites like eBay and steal your passwords. This malware usually comes disguised as phony "updates" to Adobe Flash. It looks very official; you'll go to a Web site and you'll see a realistic-looking message. complete with official Adobe logos, that tells you you have to update Flash. It will download an updater program that also has realistic Adobe logos and looks very official.
But it is not a Flash update. It is actually a program that searches for certain popular Web sites in your browser address bar, such as PayPal or eBay, and then tries to redirect you to fake sites that steal your passwords.
Have you done any updates like that lately?
