What's the firewall? This might just be referring to kernel32.dll which is usually fairly harmless. It's an old file which might just be trying to find a router or something similar...
Thought so - it's probably transmitting an ICMP packet which is used to control messages to hosts. It's probably harmless. I've done a bit of searching on the techy forums and this seems to be the general consensus...
Do you have any spyware removal/protection software installed? The more common use of personal firewalls has driven virus/writers hacker to try and exploit kernel vulnerabilities, so it is always worth checking that there's nothing on your system which you didn't put there yourself!
try visiting this site..some useful tools to check your system..i would reccomend "hijack this" but use with great care...it can cripple systems if used incorrectly.