You need to change your settings in the Zone Alarm program.
I'm trying to access aol through the AOL.com portal, and I get prompted each time to turn on my cookies!
I'm running zone alarm, and I turn it off. I've gone to Internet Options and turned the security options to LOW, as well as manually opted to accept cookies from the PRIVACY tab. I still get the same message that I need to turn on my cookies.
With Zone Alarm off, I can access AOL from Netscape, however. If it makes any difference, I'm behind a standard firewall provided by my linksys router.