Having looked at your log i'm not very happy with the "backdoor" issue. This means that somebody in a remote location may have had access to your PC as if they were sat in front of it, and this poses a number of problems.
There is no way of knowing how many malicious files may have been dropped on your hard drive, legitimate files patched or replaced, and if security settings have been lowered to make your PC easier to infect in the future.
This makes the most sensible course of action backing up any important files and then reformatting and reinstalling your operating system.
It could be that while your AV didn't keep the primary part of this infection off of your PC it is blocking anything else from occurring, but the risk isn't one that I would be happy taking.
There is some good news in that a Factory Restore of your system may be possible. While Dell does supply recovery discs, these are a backup to an easier alternative which I have used in the past with a Dell laptop that I owned. You can find it documented in the User Manual available here
in .pdf format.
The bottom of Page 41 "Using Dell PC Restore by Symantec" will walk you through the steps in running this utility which will restore your PC back to the time that it was first turned on when brand new - please note that you will need to then pay a visit to Windows Updates to reinstall whatever was released after this time.
I suggest that you download the installation files for both an anti-virus and firewall BEFORE you run the restore utility as you want to install both before you go back online. You will obviously need to check for updates once you have your system back up and running to keep your PC as safe as possible. Should you need them I can provide links to free software fro both tasks.
If you have any questions please ask - i'll answer if I can.