I run Slackware 14.1 32-bit non-SMP on a Dell Latitude D505 with 256MB RAM. KDE won't run with so little RAM. It'll come up, eventually, but you'll regret having bothered. XFCE will run if you can tolerate long delays. I do as much as possible from the command line. I use Fluxbox if I have to have a graphical environment. It's still pretty slow, mainly due to paging. Running any browser is going to cause paging with so little RAM. Don't expect to open more than one or two Firefox windows with one or two tabs at a time.

I may eventually upgrade the RAM to 2GB if I can find some for free or for next to nothing. But this is really just an emergency system that I rarely use, so again, maybe not.

I find it interesting to recall how well Windows XP ran on it with only 256MB RAM back when it was new.

It shouldn't be that much guess work to run a 10yo bootable linux iso on a 10+yo computer. Having a functional burner to create that disc with probably is a lot of guess work 10+ years later. And it's not that ideal once you start to "connect" to a network and "try" to upgrade. But it's a starting point when there might be no other option available.

My D505 has a CDROM drive, and even though it's ancient, it will still burn a CD. However, I don't bother with CD for installing the OS. I just set up a TFTP PXE boot server on my desktop system and used PXE to do a full install. For upgrades, I use NFS to mount a mirror of the Slackware distro.

Incredible!
 

Thank you so much for all the advice guys. I heard that Linux lives in a vibrant, responsive community but I never imagined getting such a fantastic response! I think (as some of you have indicated) that it is my CPU that does not support PAE. I have some more details about the specification:
Dell Latitude D505
Pentium M 1.60MHz/600MHz
512Mb RAM (I might be able to scrounge another 512Mb too)
Video Controller Intel 855GM/855GME
Audio Sigmatel 9750
Modem Conexant D480 MDC (but I never intend to use this !)
HDD 60Gb
CD-RW/DVD combo drive
I can see from your replies that there is quite a lot for me to try, but I do feel a whole lot more confident now (thanks) so I guess it would be best to run a distro from CD or DVD in order to get a feel for Linux and to establish how to make my creaky old machine run as well as it possibly can. I don't really want to do anything too heavy with it. Just play with the OS a bit, get to know Linux, use it as a bit of a jukebox probably too.
I am doing this at work, so I'll have to put it on a back burner until after the Christmas break but I will keep an eye on this thread and keep adding to my "to do" list!

Many thanks again, and have a fantastic Christmas one and all !

No. I test all the distros I recommend and I read their documentation. :tisk:

As for Bodhi, if you go to their downloads page you will see two 32-bit versions, one of which is non-pae. If you failed to get Bodhi to work, either you got the wrong one or the problem was something else.