Q: problem to login in web sites with safari, chrome, firefox

hello to you,

after serveral problems to access to different web sites, so i decided to format imac and re-install Yosemite.

Actually i have 10.10.5 installed, just formatted imac with safari, chrome, firefox updated.

No other app installed, full clean installation by usb installer, downloaded yesterday by appstore. (hard disk formatted for clean installation)

imac version: 21.5 late 2012, 8 gb ram, fusion drive 1 tb

Just re-installed yosemite, I tried by safari to access to www.ebay.it and other e-commerc internet sites, but it's no possible to login.

anytime I tried to login, re-prompt login page, without error.

i already try to reset passwords, withiout results.

the cookie is clean, imac just re-installed 10.10.5 today

i updated by appstore security update for yosemite, today.

i installed last java form here > https://www.java.com/it/download/faq/java_mac.xml

no error.

i access without problem only to google and youtube internet sites.

no problems to access all sites with iphone 5s or ipad mini 2.

can you help me to fix this great problem?

thanks in advance, best regards.

Andrea