I never trust the machine after it's infected. Even after all the antivirus and antimalware said it's cleaned.
opting for full restores, can save a lot of precious time and money.
back up files as necessary, intensive scans well advised for severely damaged systems.
if the partition(s) is really bad, write 1's and 0's to the entire drive and perform hardware health test(s).
also, keep it mind, infections (hives, spreading) may be in more than just the pc that was noticeably infected, such as routers, hubs, external drives, networked OS's, 3rd party equipment, and unpatched/secure connections. there are too many exploits out there to name that go unnoticed until the public/private sector get hit bad enough, but not everyone is a lucky-lucy.
and for those not running any kind of antivirus/firewall/security patching, to this day and age -
...the underlying question is, if ebay, target, banks and other small/large organizations were compromised at one point for a number of exploits, what makes us think that current/future exploits aren't going to target "less-secure" operating systems/hardware? any kind of security is better than none, even if you're going to run absolutely no AV on a VPN-tunnel router, the VPN is still better than nothing. even the default router firewalls are better than being on straight open DMZ. that is, for baseline usage.