For $200, you won't build a gaming computer, so I'll speak in strict HTPC sense.
Any modern computer can handle 1080p decoding just fine - especially since your parents will be essentially running just 1 application.
CPU - Use any dual-core.
Motherboard - Don't cheap out too much with this, get a motherboard with decent onboard sound (it's usually Realtek). And no, the sound is just fine, and their drivers work better than Creative's.
RAM - At least 2GB
GPU - You can actually use onboard for this, as long as it's a modern chipset (Core 2 Duo era and on). EDIT: I just read you have a spare 4870. Sure, stick that in.
HD - A single drive is fine
Case - if you need to put your 4870, the nMediaPC 6000B might fit it (you might need to break out the dremel though). It looks great, but yes, it is flimsy.
Connectivity - This is a little tricky depending on your set up. If you need to put audio over HDMI, you need to make sure your motherboard (or GPU) supports it. If you're putting audio over optical instead, just check the motherboard if it has that output. Also, check what your sound system can decode - if it's an older system that only supports, for example, AC3, you'll want AC3 Filter.
Also note since it's a HTPC, you probably want to cool it as passively as possible (large aftermarket heatsinks, large low-RPM fans).
I also have a work log of my own HTPC, but since I posted it on a "rival" forum, I can't link it to you here. PM me if you want to see it.
Thanks for the pointers though
And that build log would be sweet, send 'er over.