You *have* been hacked. The changes don't have to be noticeable to be there. If you open the html source of any of your website's pages, you will more likely than not find some html added there by the above code snippet which shouldn't be.
What's been added to the php files is obfuscated php code and no real WP core file will ever contain obfuscated code.
Re-download WordPress, unzip and upload the 'fresh' copies of the changed files to replace the hacked ones. Better yet: re-upload the whole of WP.
Also check that your .htaccess file has not been changed, that there are no extraneous files in your file system and that no extra users have been added to your database (especially with admin access).
Hope this helps.