I previously updated both mine and my fathers TomTom 720s with new maps (v880) from this site. Both worked fine for the last six months but now my fathers TT has failed (I think). It will not start without the SD card in place and when I go into windows explorer it has allocated drives to both the hard drive and SD card but clicking on the hard drive I get the message - please insert a disk, etc. I can't even format, etc.

Therefore, I decided to put everything on the SD card (navcore and maps). Using TTHome I downloaded the latest navcore (9.430) and the TT starts but obviously has no maps. I can't find any back up of the original maps and would like to use new ones anyway.

So the question is, can I download maps and use the fast activation or keygen if both the navcore and maps are on the SD card (i.e. because the hard drive is gone)?

As long as it has a bif file it should work.

Makes no difference if you use the internal drive or the SD, once a SD with Navcore and map is in the device will boot only from SD.
But you can replace the HDD with a CF memory card and an adaptor, This way you get a fully working device and even faster speeds than with the old HDD in place.
Might be worth to replace the battery at the same time ;)

I have had a couple of tomtoms with internal flash failure and they have worked ok from the external sd albeit slower to load from scratch.

I haven't been brave enough before to try and replace the HD with CF and adaptor but I might just give it a go. I remember seeing a tutorial where an SD was soldered on but not a CF. I assume there is room in a 930 to do this - would you have any more guidance?

The soldered SD is not for your model.
In fact it is so straight forward I did not bother to post a tut for it.
You can use the instructions on how to dismantle your device as a start.
Once opened you'll see the little HDD.
All you have to do is unplug,
for the HDD you connect the CF to Zif adapter and insert the CF card,
done.
If you check around on Ebay you get a 16GB CF card for abot 15 bucks and a suitable zif adapter like [Please Register or Login to download file] is under 5 bucks.
In case the battery is no good you can transform your device into a next to new device with more speed than before.
Just make sure you get a fast CF card and use a bootloader 5.5112 or higher.
Be aware that you should use one of the NC versions I uploaded with CF support, like the [Please Register or Login to download file] .
Most normal NC's won't work properly from a CF.