I finally did it, thank U everyone for support, so it was kernel problem after all. Last advice made it through. First I just reinstalled lilo but it wasn't enough. So here is what I did:
Get slackware install cd(I think it's the best to get exact version u were using before, in my case it was 13.1). Before starting setup run "pkgtool" and cleanup messy packages u're planning on reinstalling anyway(in my case it was lilo and kernel).
Then, run setup, as colorpurple21859 said, run through setup routine but do not format your partitions, just mount them in a setup process, then select packages u need to install, I've deselected almost all and left only what's related to kernel and lilo. So and that's about it, I've got my old huge kernel and what's left to clean up a lil in my system. All my old configurations are present and seems to work(too excited right now, so can't check everything, but apache and my some crucial rc scripts are working the way they used). So that's about it.
So, with upgrade all I've got new kernel 220.127.116.11 and now I'm on my old 18.104.22.168.
Once more, thank U everyone for Your support.