It looks like the computer is clean, to me, as far as it's possible to tell.
What I'd do now is have a look at, maybe bookmark
This tutorial on securing a home wireless network.
Microsoft have an article also. There are plenty around.
Go to
www.secunia.org and at least perform an online scan for software vulnerabilities.(OSI). This will help ensure that you know what needs patching. Chances are that there are some apps that are out of date on the family computer, and maybe yours, too.
Personally I downloaded/installed the PSI from secunia. Set/forget it, and from time to time, react to a vulnerability report. (Like an out of date flash player, or old Java version present.)
Have a general look at the prevention tutorials I linked in reply #6. And consider the suggestions at the top of that reply, regarding setting passwords. It's a good idea for users to have their own limited user accounts, and just leave the admin account for installing software/updates etc, but that can get complicated, and be a bit of a
PITA for ordinary users. It's probably more appropriate for just the young "click-happy" users to have to have their own accounts (limited user) and that way infections are limited in what they can do, and easier to clean up. (The infection can not progress beyond the users' profile to the heart of the operating system, normally.) See "user accounts" in the control panel.
Just remember, you can do anything you want on your own computer, but remember to seek approval for any changes made to the home computer, which might mean having read and understood the articles well enough that you can basically explain the reasons for doing so to a layman. That's actually not too hard. It's all pretty commonsense stuff, really, just when you buy a computer, the vendor doesn't tell about how to maintain or secure it beyond the basics. (If you're lucky.)