Internet explorer keeps closing and popups

Double-click RogueKiller.exe to run. (Vista/7 right-click and select Run as Administrator)
When it opens, press the Scan button
Now click the Registry tab and locate these detections:

• 
  [RUN][ZeroAccess] HKLM\[...]\Run : IndexTray.exe ("C:\Program Files (x86)\Sharp\Sharpdesk\IndexTray.exe" /n [-][x]) -> FOUND

Place a checkmark each of these items, leave the others unchecked.
Now press the Delete button.
When it is finished, there will be a log on your desktop called: RKreport[2].txt
Attach RKreport[2].txt to your next message. (How to attach)
Do not reboot your computer yet.

Now rerun Hitman and have it remove all the PUP's.

Reboot and rescan with both RogueKiller and Hitman and attach those logs as well.

Tell me how things are running now.

 

What are all these temp files on your C: drive:

Code:

C:\11EB.tmp
----a-w                 0 2013-06-07 14:42:46  C:\14EC.tmp
----a-w                 0 2013-06-10 20:20:13  C:\155F.tmp
----a-w                 0 2013-06-07 14:42:46  C:\1687.tmp
----a-w                 0 2013-06-13 15:27:41  C:\1A07.tmp
----a-w                 0 2013-06-13 15:27:41  C:\1A28.tmp
----a-w                 0 2013-06-10 20:30:05  C:\1CFD.tmp
----a-w                 0 2013-06-10 20:30:05  C:\1F24.tmp
----a-w                 0 2013-06-10 20:30:06  C:\214B.tmp
----a-w                 0 2013-06-07 14:42:51  C:\26EE.tmp
----a-w                 0 2013-06-13 14:01:57  C:\272F.tmp
----a-w                 0 2013-06-07 14:42:51  C:\29EF.tmp
----a-w                 0 2013-06-13 19:03:35  C:\2A25.tmp
----a-w                 0 2013-06-13 19:03:35  C:\2A46.tmp
----a-w                 0 2013-06-10 20:30:11  C:\34CD.tmp
----a-w                 0 2013-06-10 18:43:09  C:\35F0.tmp
----a-w                 0 2013-06-10 18:43:09  C:\3601.tmp
----a-w                 0 2013-06-10 20:30:12  C:\38C8.tmp
----a-w                 0 2013-06-07 14:42:56  C:\3C92.tmp
----a-w                 0 2013-06-13 16:06:04  C:\3DB6.tmp
----a-w                 0 2013-06-13 16:06:04  C:\3F32.tmp
----a-w                 0 2013-06-13 16:06:04  C:\4040.tmp
----a-w                 0 2013-06-10 20:30:16  C:\490B.tmp
----a-w                 0 2013-06-10 18:42:56  C:\4DA.tmp
----a-w                 0 2013-06-13 16:06:09  C:\5097.tmp
----a-w                 0 2013-06-12 18:43:34  C:\5177.tmp
----a-w                 0 2013-06-12 18:43:35  C:\52F2.tmp
----a-w                 0 2013-06-13 16:06:09  C:\5389.tmp
----a-w                 0 2013-06-12 18:43:35  C:\5401.tmp
----a-w                 0 2013-06-10 20:20:09  C:\584.tmp

(Partial list)

Plus you need to clean out the multitude of Temps in your temp folder. So run CCLeaner.

I am not finding any other malware.

Have you installed a pop-up blocker?