The follwoing was extracted from:

http://www.pchell.com/support/poweredbyzedo.shtml

for dealing with a popup problem that creates files called core.sys and core.cache.dsk in the
windows/system32/drivers folder.

The customer's computer had a current version of Norton Internet Security 2006 and he had also used Spyware Doctor by PCTools to remove the problems. I used all the basic tools at first to try to remove them including SmitRem, CWShredder, SmitFraudFix, Lop Uninstaller, Look2Me Uninstallers, VundoFix, etc. but nothing seemed to touch this infection.

On to the Online Scanners...First I tried Housecall, then Panda ActiveScan, nothing was found...Finally I tried Kaspersky Online Scanner and it found a Rootkit (Rootkit.Win32.Agent.EQ) infecting a file called core.sys in the c:\windows\system32\drivers directory.

Upon further investigation, I also found a second file called core.cache.dsk that was related in the same directory. The core.sys file had registered itself as a service and was starting automatically each time Windows booted. Because of such a generic name, it didnt appear suspicious when I was examining the running services early on in the investigation.

How to Remove Core.sys

Follow the instructions below to remove core.sys and core.cache.dsk and rid your computer of the "Powered by Zedo" and other ads.

1) Boot into Safe Mode
2) Click on Start, Search, and choose All Files and Folders
3) In the all or part of file name box, type the following

core.sys

4) In the Look In box, choose local hard drives and click Search
5) When core.sys is found in the c:\windows\system32\drivers directory, right-click on it and choose Delete
6) Repeat steps 2-5 for the file core.cache.dsk
7) Close the Search box
8) Click on Start, Run and type REGEDIT and press Enter
9) Click on the Plus sign (+) next to HKEY_LOCAL_MACHINE
10) Click the plus next to SYSTEM
11) Click the plus next to CurrentControlSet
12) Click the plus next to Services
13) Find the folder called CORE and right-click on it and choose Delete

*** WARNING *** If the folder CORE does not exist, dont do anything

14) Close the Registry Editor by clicking on the X in the right-hand corner of the window

15) Reboot your computer in Normal mode
16) Once the computer is rebooted, open your web browser and go to Kaspersky Online Scanner by clicking on the link below. 

http://www.kaspersky.com/virusscanner

17) Scan your computer and delete any other files flagged as problems.

Your computer should now be free of these vicious popups.