The desktop right corner shows that I'm running linux 2.4.31 on i686.
Ah, you do know that 2.4.31 is the version of your Linux kernel, not of DSL? That kernel version is the same one that comes with the latest DSL. To find your DSL version, go to the DSL menu, then "System>System Stats". The DSL version should be printed in the top line of the CPU tab that opens with the stats window.
As for the boot floppy, looks like you'd better try another floppy disk, or failing that, another drive. Though having just looked up the specs on your model, it should be able to boot to a CD anyway. Check your BIOS boot settings and make sure it is trying to boot to the CD drive.
By the way, 256MB RAM should be fine for CD burning, though I admit that the cdw program is quite tricky. I found a webpage that explained the process, but I don't know which computer I bookmarked it on.