Ain't I lucky?... I got MALWARE!! HELP!!

Hello there majorgeeks admins and general helpers. I am sitting here by my parents' computer and let me tell you, was I relieved to find a site that helps semi-pro geeks like me with their malware problems. This computer has been infected for almost three weeks now, 1.5 of them with a weird system error that didn't even allow windows to boot and kept restarting the computer.
Well, I finally found the time to come over and look at it properly, fixed the OS and then got stumped. Weird messages about the computer being infected with all sorts of things constantly popping up and directing me to spyware and anti-virus commercial sites, my IE home page hijacked without any hostage-taker demands to negotiate its safe return, and my mother's account desktop display showing a big red bio-hazard sign (with yet another automatic refferal to those damn sites), scaring her into not touching the computer or even entering the room it's in. So I started with some preventive
measures:
a) Ran a full system scan with my norton anti-virus.
b) Disabled my mother's administrative status (worst infected user).
c) Tried to hunt down the malware in the registry and deleting and removing any suspicious programs and files (while backing up in advance, of course).

These steps helped me fix the problem once before.
But not now.
So I Googled one of those damn program names and found you guys.
I'm not used to asking for help in these matters, so I read as much as I could and then went ahead and performed all the preliminary scans and got all the log-files ready for delivery. Took me all night and I simply went to sleep for a few hours somewhere in the middle of this.
This process did not seem to completely solve my problems. First, the main message that kept popping up during all the hasle popped up once more after rebooting(even if only once - that in itself is a blessing), then my norton keeps informing me, about every minute, that it's blocking a trojan horse (although I don't get how one of those could fit through the doorway, let alone the LAN cable ).
So now here I am, submitting this thread, asking for HELP!!
Some info: OS is WinXPpro, there are five users, Norton anti-virus installed and running. Oh, and I'm writing to you from Israel, so we may not be exactly in sinc concerning waking hours.
Anyway, this is it and I'm thanking all of those willing to help in advance. You are performing a great service, world-wide.

 

First batch of files:

P.S. : I seem to have some extra trouble with my windows explorer. It closes any open directories every couple of minutes. Another symptom of "whatever", no doubt.

 

Scan-files 2.0

Second batch of scan-files.

 

Message for Chaslang:

Hi there.
This being Israel and all, our work-week starts at sunday, so I won't be near my parents' computer till "Erev Rosh Hashana" (Jewish New Year's Eve).
...
...
Which will be on Wednesday!!!
So I'll post you then.
Thank you very much and HAPPY NEW YEAR!!

 

Hello again!
I did as asked, that is I removed CounterSpy and ran the ComboFix.
So far, it seems that the fix worked and that my parents' computer is clean once more. Here are the logs.
'Shana Tova' and thanks again!

 

And here are the rest:

 

Thank you, chaslang.
I have taken all appropriate steps to insure this will not happen again.
Everything seems to be O.K. now.
Allthough there seems to be one other problem: When I fixed the computer after the first infection and general meltdown I had to fix the Windows using the installation disk. Now I continually get a windows update icon that informs me that I need to install windows installer 3.1 .
I know for a fact that this is an important update, but it seems to be unable to install itself in this computer. Any thoughts?
And again, thank you for your help.