Use the non-smp kernel, that one is compiled without PAE.

Slackware didn't install. I knew it when at some point the installer complained about not being able to recognize my graphics chip.

It ended up with restart (reset?) loop.

I probably made some other mistakes too by canceling some setting. I didn't get back but went to the next phase.

Just like with Red Hat ~30 years ago, except no need to manually edit X configurations for graphics and display (figuring out the resolutions and clocks was a P.I.T.A).
Very nostalgic experience anyway. :-)
I think I'll try again as soon as I have time.

Some weird glitch.
This morning it installed fine.
Even with KDE it installed and booted in about the same time OpenSUSE took to boot from LiveCD!

Great! If I understood you correctly, you now have Slackware running!?

From your earlier post I was not sure what to think of it, an unrecognized video card should not prevent installation.

It may be morning for you - but it is midnight for me and I am closing down. Hope all goes well with it, please let us know whether you have problems or not, and post any questions, I'll check in tomorrow!

EDIT - By the way, please post the output of lspci if you would, pluse memory size and maybe disk setup, just so we know what other hardware you have. Good luck, I hope that you like it!

Yep, with KDE, although had to 'startx' - it booted to command line. Not really even a nuisance.
This time no complaints about the graphics or anything else during the installation.
(This time I used defaults almost everywhere.)

The machine is IBM THINKPAD T42-2373-F2G
Intel Pentium M 735 / 1.7 GHz
AGP 4x - ATI Mobility Radeon 7500 - 32 MB DDR SDRAM
Intel PRO/Wireless 2200BG
And a funny CD/DVD that reads and writes CD/RWs, reads DVD-R and RVD+r and can't even read rewritable DVDs.
1 GB RAM (max 2GB) and HDD changed to 160GB (max.)

I guess in case of questions/problems I'm now qualified to ask in the Slackware-forum. ;-)
(Currently at work.)

Great, thanks! Slackware will be happy on that one!

Yes, Slackware boots to the console by default, a simple edit of default runlevel in /etc/inittab will take you to a graphical login. I spend much of my time in console with tmux'ed shells and prefer to start x only on demand, your prefs may vary.

You can try other DEs by changing the client to startx (Ex: startx /etc/X11/xinit/xinitrc.fluxbox, my choice). To change the default simply change the xinitrc symlink in that location, or edit your home ~/.xinitrc

Be sure to create an unpriviledged user an not run X as root, etc. etc...

Welcome to Slackware and the Slackware forums!

No worries. I used SunOS and BSD Unix in the 90's.
I kinda got used to login and say 'startx' - if I wanted to do something using GUI.
Nothing really needs to do with it. I think I might even like it better this way
(after all these years).

Actually, you can have a reasonably stable roller that is suitable for a serious productivity machine, stick to the stable repos if using Arch or Manjaro, or the stable Portage tree if using Gentoo, instead of using unstable repos or Portage trees, and stick to official repos or sources as much as you can, like you would in Ubuntu, for example, on the fixed-release side, stick to the stable release and avoid PPAs as much as possible. Also, running the LTS kernel can help as well, although that's optional as the stock kernel works just fine.

Also, learned the hard way that running unstable repos can give you hell regardless of whether you're running a roller or a fixed-release distro, ran the testing repos both in Fedora and Arch, had a lot of breakages in both. Most recent breakage in Testing I experienced, a GTK2 breakage, which prevented me from logging into MATE, as in it booted me right back to LXDM whenever I attempted to login, was pretty much the last straw and I've been running just the stable repos since. No major breakages so far.