The first time I did an update that upgraded the kernel, I had a similar experience. My solution may or may not help; I buy the Slackware installation disks as I love the product and really want to support it any way I can :-) When the kernel gets upgraded, I put the bootable install disk into the cdrom drive and reboot with CTRL+ALT+DELETE. When the installer boots, log in as root (no password required for the installer). Then run setup. Then Addswap, then Setup target partitions (DO NOT format your partitions, or you will lose everything they contain). Finally, Configure your system. After that, you will have to go through all the steps to switch to a generic kernel again, using the freshly upgraded kernel. Note: do not do the Install, or you will end up with the original unupgraded version.

I got it solved now, it even more of a mess than I thought...

I'm from Slackware 14.1, and in 2016 I did the update towards 14.2, but it turns out a problem remained dormant, most notably in slackpkg, who still believed due to a misconfiguration that I was on 14.1, so it didn't only downgraded the system libraries, but also deleted the god forsaken kernel, leaving me with a huge brick as a computer, turns out I was able to backup most of my files thanks to a live USB, so I resintalled and reconfigured Slackware, and it now works better than ever... Turns out a reinstall is definitely way better than an update....
Thanks for the help dudes !