Multiple Issues Found

Based on your logs, your problems are not related to malware. But there is a little junk to cleanup so let's do that.

New version of RogueKiller is out and changed things. Check for a log in this folder >>> C:\ProgramData\RogueKiller


Uninstall the below programs. If you do not find them or they will not uninstall, just keep going.
Java 7 Update 9
Now install the current version of Sun Java from:

• Go here for 64 bit OS = Sun Java 64 bit Runtime Environment Make sure that when you see the form asking about installing Ask Toolbar that you uncheck this.
• Go here for 32 bit OS = Sun Java 32 bit Runtime Environment Make sure that when you see the form asking about installing Ask Toolbar that you uncheck this.

Make sure that when you install the new version of Java that you uncheck the Install the Ask Toolbar junkware checkbox. You do not want to add the stuff junk that most people consider malware to your PC. Also just in case Oracle changes the Java installation in the future to possible install other junk, uncheck all but just installing Java.

Please download OTM by Old Timer and save it to your Desktop.

• Run OTM.exe by double clicking on it (Note: if using Vista, Win7 or Win8, don't double click, use right click and select Run As Administrator).
• Copy the lines from the below codebox to the clipboard by highlighting ALL of them and pressing CTRL + C
  (or, after highlighting, right-click and choose Copy): Do not include the word Code: which is just a title line of
  the code box

Code:

:Processes
explorer.exe
 
:Files
C:\windows\tasks\Default Scheduled Scan (no edit).job
C:\windows\tasks\GoogleUpdateTaskMachineCore.job
C:\windows\tasks\GoogleUpdateTaskMachineUA.job
C:\windows\tasks\GoogleUpdateTaskUserS-1-5-21-2048175547-843909783-4265755947-1000Core.job
C:\windows\tasks\GoogleUpdateTaskUserS-1-5-21-2048175547-843909783-4265755947-1000UA.job
C:\windows\TEMP\*.*
C:\Users\Remy\AppData\Local\Temp\*.*
:Reg
[HKEY_LOCAL_MACHINE\software\microsoft\windows\currentVersion\Run]
"HP Software Update"=-
[HKEY_LOCAL_MACHINE\software\Wow6432Node\microsoft\windows\currentVersion\Run]
"HP Software Update"=-
[HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\SearchScopes]
"DefaultScope"="{0633EE93-D776-472f-A0FF-E1416B8B2E3A}"
[-HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\SearchScopes\{39EBE947-7D13-4732-9964-05F8F982C108}]
[-HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\SearchScopes\{BAB5A99A-AB9B-4F03-8AE2-714F2C137DF0}]
[-HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Browser Helper Objects\{02478D38-C3F9-4efb-9B51-7695ECA05670}]
:Commands
[purity]
[EmptyTemp]
[start explorer]
[Reboot]

• Return to OTM, right click in the Paste List of Files/Folders to Move window (under the yellow bar
  ) and choose Paste.
• Now click the large button.
• If OTM asks to reboot your computer, allow it to do so. The report should appear in Notepad after the reboot.
• Close OTM.

Now navigate to the C:\_OTM\MovedFiles folder ( assuming your Windows drive is C). This is where your log will be
saved in the form of Date and Time mmddyyyy_hhmmss.log. Just look for the most recent .log file. Attach
this log file to your next message.

Now please download Junkware Removal Tool to your desktop.

• Shut down your protection software now to avoid potential conflicts.
• Run the tool by double-clicking it. If you are using Windows Vista or Seven, right-mouse click it and select Run as Administrator.
• The tool will open and start scanning your system.
• Note: That JRT may reset your home page to a google default so you will need to restore your home page setting if this happens.
• Please be patient as this can take a while to complete depending on your system's specifications.
• On completion, a log (JRT.txt) is saved to your desktop and will automatically open.
• Attach JRT.txt to your next message.

Now run the C:\MGtools\GetLogs.bat file by double clicking on it (Note: if using Vista, Win7 or Win8, don't double click, use right click and select Run As Administrator).

Then attach the below logs:

• the C:\_OTM\MovedFiles log
• the JRT.TXT log
• C:\MGlogs.zip

Make sure you tell me how things are working now!