Then I'd take them down to the local electronics shop and they'd use that magic ring thing on them (it almost DOES look like they're doing magic) and then they were all better. I'm guessing the degaussing circuit on monitors is something similar?
Yep. You can make your own degausser('Magic Wand') fairly easily. Build an electromagnet capable of taking 120 volts, put a plug on it and plug it in.
Degausers work on the principle that it's slightly easier to demagnitize something than to magnetize it. So you hit what you want to demagnetize with alternating fields(electromagnet hooked up to AC will work just fine). That and field strength is less the further away the magnet is, so you gradually pull it back once you've gotten rid of most of the magnetization before you switch it off (so you don't get that last polarity).
edit: The air purfier might be using DC for something, is it an ionizing purifier?