Assuming the motherboard has most of the same features/capabilities as the old one does, and you are reinstalling the original system discs, then probably not. Video chip sets may be the biggest issue. If that changed significantly, then you may need to boot from a rescue CD/DVD and change the video driver settings in /etc/X11/xorg.conf.
What do you mean by same features. What if it's a different Socket / Ram ? The same goes for Windows Vista/7 I was informed that all that would be needed when that time comes for Windows was to change the chip set, but that sounds too easy !
I believe if your mother has different chipset, sound chips, network adapter, and vga card you may need re install them. To what I know you don't have to completely re install linux. In Ubuntu 10.10 assuming it is currently install. All you have to do is go to System > Administration > Additional drivers. It will detect your hardware and download the appropriate one.
I have transfer my hard disk to several computer which was Pentium 4 machine and 32 bit Linux OS. But I believe you cannot transfer 64 bit to Pentium 4. Maybe due to architecture design. More research need to be done. But for Window XP, most of the time you need to re install Window XP. Don't know about Window Vista or 7 though.