RHs and Knoppix seem to work all right...but when I try to put Arch in, or any other distro (seems so), I get this warning at bootup telling me:

"kernel panic: vfs: unable to mount root fs on hdaX" where X is the partition number of my /-filesystem.

and there it hangs - reboot button is needed. some distros' installation won't even start, some distros' will - but always it ends at bootup, if I get that far. Why? How can I fix this?

Make sure you have support built in for your ide device and for root file system.
Also make sure your kernel has a root= parameter passed to it in your bootloader (lilo or grub?) and that the parameter points to your root file system.

yeah, I've triple-checked that root= line (using grub), ought to work..the trouble with the kernel is, even if I manage to get to the point where I can compile a kernel of my own choice, how would I know what's wrong? I've tried this actually, only to end up with the same error, even after I thought I checked and selected the stuff I need for ide and fs...

this is a bit frustrating, as I've suffered this problem for over half a year now :/ and RH9 isn't the best distro for a home pc these days...

does this happen when you use the arch disc to point to your / to boot up?

yes...I've tried to check and I'm pretty sure grub's config file is correct and points to the right place. I just don't get...I tried starting the install again yesterday, but Arch didn't even start the installation...the kernel which is used to boot the installation, doesn't work. now I'm a bit confused..I might be able to work this out if I had a working kernel for the installation, but it's no use if the installation-cd's kernel won't work.

might you have ideas where/how could I obtain/make/build/do magic stuff to get an installation disc that would boot, so that I could actually (during installation) compile a custom kernel?

the only working kernels this far have been the one of Knoppix's and the ones of RH and Fedora. Arch's kernel differs in some way from them....

You may want to make a post over at the archlinux.org forums. The guys there are very helpful and should be able to sort you out.