You should definitely try to get the data off your drive using firewire target disk mode if your drive is not too badly damaged to mount in FTD.
Diskwarrior might well rescue your drive since the S.M.A.R.T. status does not suggest a hardware failure.
On the other hand, for the price of DW, you could probably replace the drive in the eMac altogether with a newer and bigger one, put the old drive into an external USB case, install OS X on the new drive, then use migration assistant to restore the data and settings from the old drive.