For once, I can post something I found out that's useful!
I have a couple of external drives - one gets plugged in once a week to back stuff up.
The computer knew it was there because it showed up in the "safely remove hardware" dialogue but otherwise, it didn't show up anywhere - certainly not in My Computer or explorer.
So I looked at the properties, and change it from being "optimise for quick removal" to "optimise for performance".
And voila, there is it! Woot!
Thank you Janet! I'll have to remember that for when I finally get my external caddy working reliably.