I've been upgrading my kernel every stable release beginning with 2.6.37.4.

I somehow bungled my current source, 4.14.10, and couldn't build.

I had the full source for 4.13 on hand. I built that successfully. Then I patched it with patch-4.14 and built that successfully. Then I tried to patch that with patch-4.14.10 - but that patch complained at every step: failing to find target files, not finding the target code in the right place.

I'll download the full source for 4.14.10, but I'm curious about what I may have done wrong.

If you're using the patch from kernel.org 4.14.10 patch is from 4.14.9 to 4.14.10, it means that in your case you'll need the other ones too (4.14.0 o 4.14.1 etc). You can download all the patches from https://cdn.kernel.org/pub/linux/kernel/v4.x/ and if you apply one by one it should work fine.

I was using the correct patch. I had made another mistake. Sorry to ask prematurely.

It's a lot of extra work to install the incremental patches, 1 by 1. patch-4.14.x is the cumulative patch, upgrades 4.14 to 4.14.x