The easiest first: is your antivirus/antimalware up to date. Then try reinstalling the browser on one of the clients.
This appears to be a security certificate issue affecting all of the WinXP IE8 clients only. The issue appeared simultaneously late yesterday on at least 6 clients with the WinXP IE configuration. The issue has so far affected only two websites out of hundreds so far in the last 24 hours. The affected websites are GoDaddy.com and a subscription financial services website. The MS Vista and Win7 clients with IE11 and FireFox are not affected. The same clients with the WinXP IE8 configuration do not have this issue while using FireFox as the browser instead of IE8. The clients have variously been online as much as 24/7 and offline as much as 9 months, so the question of problems with updates to XP and/or IE8 appears to be excluded as a potential difference.
With respect to anti-virus and/or malware software, none of the 6 clients tested have the same configuration or much of anything in common. They either have no anti-virus software or have different versons of malwarebytes.
GoDaddy tried to make GoDaddy.com a trusted site, which had no effect upon the problem. Clearing the browser caches across the six clients has no effect upon the issue.
GoDaddy says they have received no other reports about a problem with this configuration, so they are assuming it is a “local issue” until they receive more reports from other users at other IP addresses. So, the purpose of the post was to further the process of elimination by determining whether or not anyone else using WinXP with IE8 is experiencing the same “security certificate” error message when browsing at godaddy.com?