It would be nice if you could still use the old machine, however as MM suggests, it would seem that if the mother board no longer wants to co-operate, then it probably won't be able to provide you with the data path to the new 'puter.
Vulcanised's advice seems to be the good option. An external HDD caddy or docking device should do all you require.
However it needs to be able to work with the data port used by your old HDD (SATA, IDE - or something else perhaps), and of course it needs to be able to operate with the Mac operating system in use in the new machine. Such devices seem to be readily
available in Australia (at least with SATA connections), so I'm sure you would be able to source them elsewhere.
Good luck,
FoR