Ah well... it was worth the query, at least.
I think that to start with, I'll install a spare, boring PCI ethernet card that should be old enough to be supported by Linux, but new enough to be supported by Linux.
Once I have network access from the new box, I'll see about downloading and building the newer kernel.
Thank you *very* much for your answers, and especially for the speed of those replies!
-- jt --