Restore from a backup.
Sorry, but really if they are irreplaceable why haven't you got a backup copy, what happens when the disk dies as they do from time to time?
I presume the new mobo is not the same model as the old one, this means XP's low-level chipset drivers can't initialise the board and hence XP can't boot. In theory you could re-install and overwrite the current Windows tree while at the same time preserving your files, in practice I personally have never tried it.
For complete safety, in the absence of any backup, I'd get a new disk, install on to that and then copy the files you need off the old one. This of course presumes you have a full XP install CD and not one of the crass 'recovery CDs' one gets with new machines these days.
If you've a CD/DVD burner and some DOS-based software you may be able to save the files to optical media.