Problem: multiple windows for IE. I interpretted your problem to be 2 windows for IE after making just a single request to open IE.
"Cloaker" appears to be legit from the OEM.
Reset IE (link from recent post by kimsland)
http://support.microsoft.com/kb/923737/en-us
From a malware perspective, the R0/R1 entries are ignored by me. The IE reset should clean these out (and probably other entries related to browser). HJT logs normally have fewer R0/R1 entries. HOWEVER, since responding to this thread, I encountered another HJT log with a similar pattern. Different but not a problem. To me this suggests something in common, but not IE8.
If problem persists, re-run HJT. Repost results.
Are you asking about using HJT? Analyze, generate a log, fix checked entries, etc.
'Fix checked entries' should remove them from the HJT log by making changes to the browser. The advance screens for HJT can restore any/all of these.
The events logs may give a clue what is happening.
Try different ways of opening the browser. It will steer the focus toward the OS or in the other direction for the mechanism calling for IE8.
I tend to be a 'generalist' - I will work with the user to find the root of the problem. Spiritwind & Tw0rld and other notables have been more focussed. They seem to be backed up with knowledge & resources that get to the problem quicker.
Since malware does not appear to be causing this, re-posting in another forum (Windows OS) with a new title descriptive of the problem may bring in different views.