The kernel problem with recent updates has been solved. Find the solution here
-- Required MX 15/16 Repository Changes
-- Information on torrent hosting changes
-- Information on MX15/16 GPG Keys
-- Spectre and Meltdown vulnerabilities
-- Introducing our new Website
-- MX Linux on social media: here
-- MX-18.3 Point Release release info here
-- Migration Information to MX-18 here
-- antiX-17.4.1 release info here
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I ended up just upgrading to MX-17. Just have some apps to re-install, and various tweaks (but yay for the MX Tweaks, that helps!), but I'm happy to have this laptop working again. The install from liveusb went smoothly, as I already had root and home in separate partitions. I watched dolphin_oracle's video beforehand (they're always quite useful). Wish I'd had the guts to do this initially, once the first few suggested steps weren't working for me! Thanks again to those who posted suggestions.