Well...
There is only ONE 100% safe way I'm afraid, and that's a DOD Disc wipe, and a bootsector scan, then a reinstallation...
very ugly, timeconsuming and with an awfull amount of lost data (stored pics, videos, emails, and basically every dosument you ever saved to the disc in question)
So let's take a look at some "insecure" but helpfull alternatives, shall we?
First: it's utterly important that you remove all network connections from your family PC..
it mustn't communicate with the internet!
No if.. it simply must NOT have a chance to connect.
(Pull the cable, remove the wireless card.. whatever it needs!)
Find a still connected uninfected computer
to find
malwarebytes anti malware (free version should do)
install it on the family computer and let it run, it'll take some time to finish most likely but it's great at detecting malware tools, and is able to stop and remove most of them without any further ado.
(maybe you need the chameleon edition.. get that too)
Chances are your installed antivirus is corrupted or disabled, so find
clamwin on portableapps.com and install it (extract) to a usb thumbdrive from the non inffected machine, update the definition files, and run it from said thumbdrive on your PC.
It's a good idea to also get
http://portableapps.com/apps/security/kaspersky-tdsskiller-portable
http://portableapps.com/apps/security/mcafee-stinger-portable
http://portableapps.com/apps/security/spybot_portable
and let them shoot too.
That way you can remove roughly 95% of all known viruses trojans and malware that's older than a month.
Leaving you just with the most advanced and/or recent viruses,
and maybe one or two malicious software tools.
Those are the bad guys you should be worried about.
Now google for
"sysinternals tcpview" (sysinternals was bought by microsoft some years ago... the tools should still be available)
and
"sysinternals process explorer"
and since we're at it get
"sysinternals pskill"
extract them to the same thumbdrive as before.
neither one of those needs installation and can be left on the thumbdrive to run on your family pc.
Wait... I linked the tools, that's a bit easier that way
Now back to your computer, run process explorer and carefully observe the running processes.
When in doubt, kill the process..
if it restarts on it's own a second later, choose "kill tree", if it still restarts, it's either a mandatory windows tool, or malicious (well few other software acts that way.. but don't get fooled by names)
write down the name and path (maybe TCP adresses etc) on a piece of paper.
repeat..
you'll notice many running microsoft apps (svchost) one or two will shut down the computer if killed.
No big deal.. remember the sub-processes they ran when you kill that tree,
and in case it shuts the computer down, reboot, kill the other one(s)
Kill as many processes and trees as you can, a stable blank windows installation should perform well enough with just a small handfull of tasks.. ten, maybe a dozen max.
(well, mileage may vary

)
Note down the few you cannot kill without crashing the computer.
if something cannot be killed with process explorer, use pskill (command line tool)
Now..
run tcp viewer and note down the adresses those processes want to connect to.
(you can see most in process explorer as well, but there's no overview)
and which process it is of course.
And now the hard part:
RESEARCH.. from the non infected machine of course,
check, double and triple check each process name, location and tcp-target.
If one is NOT flagged on any page mark it as safe on your piece of paper
if you see any "Warning" or "Danger" or "Malware" sign, see if there is a removal tool on the internet, and download it to the stick..
Right now you might want to get the update files for your installed Antivirus.
maybe even want to consider swapping to another sofot (kaspersky is good, panda not my favourite, Norton I'd not recommend [personal preference only!] I'm running a free Avira copy personally)
Anyways, update your Antivirus and let it do a full system scan
after you ran all the removal tools (or followed all removal instructions) you downloaded earlier.
again this will take a while to complete.. do not rush!, let it do it's work.
Now reboot the system and run your antivirus again (quick scan), allow MBAM another scan and finally you should have a system that's again safe to use.
open window's control panel and remove all the software you want to remove.
(especially "toolbars" are known to contain malware more often than not.. performance tools, system optimizer etc.pp)
remove the games, hacks, and whatever your kids might or might not have installed that could contain malware.
You should have spend most of a day by now but have a machine that'S finally safe to reconnect to the internets...
And you have not lost any image, no document, and no email you had on the machine.
'sid