unSpawn, my apologies for not responding earlier, but I've only just discovered the solution - and it's incredibly simple. And perhaps it's nothing to do with quotas - I really don't know.
Anyway, fiddling around with quotacheck got me nowhere unfortunately. It just made my head hurt.

Then I rather gave up because I had by then set up a quad boot (Fedora 5, SuSE 10.1, Ubuntu Dapper and Windows) on my laptop so if I wanted to use Fedora I tended to favour the laptop. I've booted into Fedora on the laptop goodness knows how many times without problem but then, this morning, the same thing happened. "INIT: Entering Runlevel: 5quotas: write mode: FAILED" All I had done was to edit my Fedora /etc/fstab from Ubuntu, putting in a line to mount a shared vfat partition. Ho hum. Detective work time. As far as I could tell the partition label on the shared swap partition had disappeared. I tried what I had tried before with mkswap, to no avail. So I changed:
Code:
LABEL=SWAP-hda6 swap swap defaults 0 0
in the fedora fstab to:
Code:
/dev/hda6 swap swap defaults 0 0
and the problem melted away. I did the same with the corresponding line in the desktop and problem gone there now too. Or at least if there is a problem, it's not telling me.

I can explain the disappearing swap partition label in the desktop, but not in the laptop. And why a muddle over swap partition labels should cause that error message is quite beyond me.
Another curiosity. I installed fedora on a second desktop, but in that it did not label the swap partition, being happy with /dev/hda5 or whatever. I wish fedora would make its mind up.
