For a while I've been thinking about something similar on a personal scale.
Take a mainboard like this one (Via NAS 7800-15LST):http://www.via.com.tw/en/products/mainboards/motherboards.jsp?motherboard_id=610
It's got 12 SATA connectors and two times GBit ethernet. Of course you'd need PATA to SATA connectors on each hard drive, at around 10 dollar each.
So, at around 1000 dollars already, as someone pointed out earlier, it's probably more economical to just buy a big new fast HD with lower power draw.
You'd still need at least 8 of these boards and probably some casing, PSUs and cables which makes the bill more likely above 2000 dollars.
Regarding the power draw... I think that shouldn't be too bad if used for backup, since the disks can be kept spun down most of the time.
While not economical for a business, for home use it might be a different situation. Especially if, like me, you don't have any real backup at all.
Put the mainboard with all your old HDs in your cellar, run ZFS on it, and voila, no worries about dying hard disks.
Only problem is you can't buy the mainboard as an end user. Oh well. Just wipe and donate them already