Can I take a hard drive from an iPod Video and put it in an older iPod?
Probably not.

You might have "form factor" issues, for one. But also, the two devices probably have different hardware, thus the software on the drives is probably incompatible.

Assuming that you don't have problem #1 (form factor), you'd still need to find a way to copy the image from the "older black-and-white iPod" over the 80GB drive before installing it back into the good iPod.

I think there are guides out there for this, but you're going to have to look around. I would start at the awesome DIY Fix-It site: http://www.ifixit.com/Guide

Otherwise, you may want to consider getting your iPod Video repaired: http://www.ipodrepair.com/