Okay question: Who cares?
I mean if you're not willing to put enough money to get something more hightech than ISA ..or you're using a PC from 1997 ....
Cmon, get with the times.
Technically speaking a kernel can operate with just enough memory for itself and it's heap which is only a few megs. Memory can be swapped out so provided you have a reliable method of keeping a pagefile it should be possible, not saying it would be very efficient (or sane).
The way I see it you need a) Enough memory for the entire kernel (few megs) b) Enough memory for some pagetables/pagedirs
One 4KBPage maps 4MB of memory, not all memory has to be mapped at the same time. I think you may also need a small window of memory for a process to run in, parts of a process should be able to be paged to the disk/reread if you mark them as non resident then put them on the disk. On pagefault they can be paged back in from a file or swap. I'd estimate 16MB at the most for a fully working kernel. (Slow as hell and your disk would be active always
Now the term "old hardware" is also very vauge. I'd call hardware released in 1999-2000 old, and I'm pretty sure XP can run on that (Since most of the PCs who upgraded to XP on it's release used something around then) so it wouldn't be a far stretch to 1997.