Welcome to DAL,
Create a folder such as C:\HJT or C:\Program Files\HJT and move HJT.exe into the newly created folder so we can have avaiable backups in case you fix the wrong thing or I make a mistake. Very important.
Your log doesn't look to bad at all, a question, are you familiar with this below:
O4 - HKLM\..\Run: [ShowLOMControl]
Your Java is out of date and there is a worm going around now that exploits your version real easy, so I suggest you get Java updated now.
Updating Java:
* Go to Start > Control Panel double-click on the Software icon > add/remove programs.
* Search in the list for all previous installed versions of Java. (J2SE Runtime Environment.... )
It should have next icon next to it: IPB Image
Select it and click Remove.
* Then Download and install the newest version from here:
http://www.java.com/en/download/manual.jsp
Open Hijackthis.
Click the "Open the Misc Tools" section Button.
Click the "Open Uninstall Manager" Button.
Click the "Save list..." Button.
Save it to your desktop. Copy and paste the contents into your reply.
So you are saying you still have icons on your desktop?