If the error message spelled kernel with an A then it probably is a trojan.
From Sygate :
"Under most cases blocking the windows kernel should not create a problem. However, in some rare instances certain Internet Service Providers (ISP) will send you an ICMP message to verify that you are online and blocking this may cause them to turn off the service. If this happens, simply enable ICMP using the Advanced Rule editor."
From PC Club Forum :
That sounds to me like you got a trojan. The kernel itself shouldn't be connecting to the internet because the trojan is diguising it as the kernel. Do a virus scan.
Run spybot search and destroy and ad-aware, then do an online virus scan. The PC Clubs thread offers a link to swatit for detecting trojans & bots. If nothing turns up, block it and forget about it. If your isp starts disconnecting you, follow the advice from sygate and allow it with your firewall. Obviously if your using a different firewall the directions will be different but it should give you some idea of what needs to be done.