Comment Re:Chromebook (Score 4, Informative) 334
I think you're going to run into a general problem here, in that modern computers are generally not built to work off of such slow Internet connections. They're constantly getting big updates and patches.
Some people have pointed you in the direction of Chromebooks, which to my knowledge doesn't have a POP3 client available because Google assumes you'll have web access. There may be other reasons why it won't work.
I think your first instinct might be best. Install Linux. Figure out exactly what applications they need, and install only those apps. You can probably hack something together to run a script when they receive an email from you, but I think you'll be better off just having them run a script manually (tell them 'click on this button') that will collect diagnostic information and email it to you, if you want to do that.
Pick a relatively stable distro (Debian?), strip it down to the bare necessities and use a lightweight desktop environment. Set it to only download security patches. For any updates more than that, bring a disk when you visit.
I'm afraid none of this will keep them from responding to Nigerian scammers. Maybe set up their email to only accept messages from whitelisted addresses? Or maybe your parents just can't have the Internet.