As I mentioned above I have x64 and have no problems with any website...I have never had a blue screen or crash of any sort...with or without KIS...Do you have all the Microsoft updates installed...There are several fixes for things in those as well...My system checks for those all the time...and auto installs...I am also running IE7 full version..
We (my roommate and I) are both fully updated and the copies of winx64 are legit. Have you been to, say www.verizonwireless.com ? If you don't have any problems there, and are running x64 and KIS, then perhaps the problem is indeed in the software environs we have here.
However, we'd been running the new KIS for quite some time before this problem turned up, so if you haven't had this happen yet, perhaps in time it will.
Though, yes, I wouldn't rule out a software environment problem, it certainly could be a conflict of some kind, though my friend and I have nothing much in common on our set-ups excpet for winx64 and KIS so I'm not certain where a conflict might arise.
The Anti-Hacker disable suggestion was very helpful, BTW, that does seem to solve the problem, though I don't relish not having a firewall up, and I trashed my old one as soon as I got KIS.