TY for this link!!! Will spend a little time digesting the info.
Meanwhile, in answer to your questions (new kernel, new software, new hardware, et cetera), the answer is always no. This is because I'm using that distro only as a live CD with a persistent home on a USB pendrive, so the basic file system is static. I am new to it (TinyMe Linux, which is a Unity Linux fork), and am just checking it out as a favor to a pal of mine. So I have not tried to install it, or even add small packages from its repos, but have only done a few cosmetic setting-type things (GTK2 theme, cursor size) which can be saved in home. It worked straight outta the box for a week straight until yesterday...
I like your idea about a missing kernel module. Will lsmod TinyCore and compare my results.