1) Buy or get your parents to buy a laptop that will fit in the longer of the 2 "medium" USPS priority mail boxes, leaving a little room for protective wrapping (costs about $11 to ship and the computers tend to survive the experience)
2) Obtain the computer long enough to install free virus scanning like MSE if it's a PC, and be sure to install LogMeIn, keep a log of all the passwords you use for LogMeIn (there is one for the account and one for each computer), and to do any other setup (OpenOffice is usually handy).
3) Setup cloud backup of documents and desktop using DropBox or SugarSync or something (parents often only need the free service), again keep the passwords.
3) Ship it back, and when you get that phone call about the non-working computer/bad browser behavior/question about whether recommended updates are real or viruses, use LogMein if the machine boots, which will let you see everything that is happening on the screen, or do it yourself!
If it will not boot/let them login, get them to ship it back to you for further brain surgery... ;-)
And so on and so on...