Hi Balmung3000,
A Trojan should not be able to get onto your system while browsing if your OS and browser are up to date and you have a firewall up.
What is your OS- Win98, 2000, XP, Vista? What is your browser and is it up to date? Do you have Windows’ firewall up or a third-party firewall like Zone Alarm or Kerio?
KERNEL32.DLL is indeed an important system file- if found in the correct location. Malware often has the same name as a system file but is found in a different location. What location did avast! report for the malware? For example: C:\Windows\System32.
The fact that this was a Win32:patched detection suggests that the malware has infected the genuine windows file. Does avast! give you the option to repair?
Try the advice here:
http://www.f-secure.com/v-descs/trojan_win32_patched.shtml
(There is a clean version of Kernel32.dll backed up in the avast virus chest: if you can access your HD from another computer, you could replace the infected file with the clean backup, but try a System Restore first, if possible.)
EDIT: Re-reading your post, I see it’s a laptop, so removing the HD and running it as a slave in another computer won’t be an option.
Other options are to scan with AVG Anti-Spyware, a-Squared and DrWeb CureIT!, and see if they give you the option of repairing the infected file.
http://www.ewido.net/en/
http://www.emsisoft.com/en/software/free/
http://download.drweb.com/drweb+cureit/
Good luck!
PS: Secunia Software Inspector is an excellent way to check for outdated and vulnerable software that can allow Trojans onto your system via drive-by downloads:
http://secunia.com/software_inspector/