Ok, you are getting ahead of us here. Let's step back a bit;
I have not done this correctly, I don't believe, because I have neglected to ask several KEY questions;

In your very first post you say that you HAD LinkOptimizer on the computer and removed it...HOW did you remove it? Exact Steps please. Did you use the removal program for this problem or manually remove it? If you DID use a program to remove it, WHAT program did you use and did you follow the instructions EXACTLY?

O2 - BHO: (no name) - {A5366673-E8CA-11D3-9CD9-0090271D075B} - (no file)
This entry is a varient of CoolWebSearch.
O2 - BHO: NAV Helper - {BDF3E430-B101-42AD-A544-FADC6B084872} - (no file)
This entry refers to Norton Anti-Virus
O2 - BHO: (no name) - {DA39029C-D291-A968-3FF4-D0990D5CB5FC} - (no file)
This entry refers to LinkOptimizer
HKLM-Software-Microsoft-Windows-CurrentVersion-Explorer-Browser Helper Objects-{BDF3E430-B101-42AD-A544-FADC6B084872}
This again is a remainder of Norton Anti-Virus.
Did you do the MANUAL search on the computer for Norton and Symantec files and delete those found?

Your log may "look" clean but your computer is not.

We really need to know EXACTLY how you removed LinkOptimizer. Every step taken and in what order.

You say in post number 4 that you "started Spysweeper". Now we did not request that you do this, but this is fine, it is an excellent program. But we would prefer that you not run a program or use a program until directed to do so. When you say you started it do you mean that you did an actual SCAN with Spysweeper or just let it run in the background? If you DID scan with it was it done in SAFE MODE?

In post number 6 you say you followed the instructions given on Phillie Phan's thread that I directed you to and that you "got rid of quite some infections"...What infections? Which program removed them and where were they located? We need to know the names as some infections, even though "mostly" removed by a particular program sometimes do need some additional removal steps that would need to be done manually.

In post number 8 you give us this information;
"The last file opened with notepad shows this nice entry:"...and then you give us the information you received...WHAT last file opened and where? I honestly have no idea what last file you are talking about. Last file of the three you noted, or last file from an information site, or last file from a particular scan?
In this very same post you say you are unable to "delete some of these registry entries with HighJackThis" or with reg editor. Please wait to edit the registry until told to do so. This will be the very last step, if necessary. It may not be necessary at all because several of these removal program DO fix registry entries also, if run correctly.
I realize that this is very frustrating and you want to get this computer cleaned up but you must wait to perform specific steps when we tell you to do so. Leaping forward, ahead of time, can make matters worse instead of better.

Now please post back with these answers;
How did you remove LInkOptimizer? Exactly.

What are the names of the viruses that were removed by using the steps in Phillie Phans instructions and what programs removed them?
Did you run Spybot, AdAwareSE, CCleaner, Ewido in SAFE MODE as instructed and have each program remove everything found?

Have you done an actual scan with Spysweeper or just allowed it to run in the background?

When you uninstalled the FamilyKeyLogger program exactly HOW did you install it?

What was this last file opened that you tell us about and how was it opened?

Do not take any other steps just yet, please just answer these questions. You ARE showing at least two trojans still on the system or at least the remnants of them, which means of course they are still there and will continue with their nasty work. But we need the answers to the questions I have just asked BEFORE going on to other steps which we will tell you to do.