If your mom pays bills from that machine , we'll start there.That's online banking.The username and password for that must be changed immediately.as well , If your mom has credit cards , those probably need to be cancelled and changed too.
As far as your dad's data goes , I'd change the email password too.You mention he does work related stuff.If he's just doing accounting or whatever you might be ok , but if there is sensitive customer data on there , it might be compromized as well.Your dad will know if it needs to be worried about.If he's actually logging into a work network through a VPN or something , that may be compromised.
This kind of infection is pretty much the worst.I'd know it's happened to me.
You really must 'assume-the-worst' as far as whats been compromised....even forum passwords or game keys .....
Do NOT plug that harddrive into your machine.Also , do not plug it into the internet again untill it's been dealt with.
Best way to get the data off that machine would be a usb memory stick.Take only data.do not take any programs.Do it slowly and concisely , don't just grab whole folders unless you know exactly whats in em.
You got the BRAVIAX ? ThaT's a nasty MF :) AVG skips on a lot - I use Spyware Doctor (that one effectively removes BRAVIAX and any strays left overs) don't attempt to manually remove them, some will show up again. Get yourself spyware doctor, you will be surprised how much stuff it finds on your system. You should have a BRAVIAX files in the %windows%system32 directory too. I use AVIRA security suite, that one also finds stuff, has an excellent detection rate, and it removes more stuff left than other programs.
I had the BRAVIAX too and neither Spybot S&D 1.6 nor AdAware 2008 even detected it !
Same for Norton, it skipped on a lot of that too.
Spyware doctor works good, indeed. I'm registered user myself.