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I don't think you'll be able to activate another instance of the same Win 7 CD key on your mum's new setup because it's technically in use by the older parts. However, the old parts & Win 7 should still work.
The general rule of thumb is that if you are installing a new motherboard or a new OS hard drive, you should reinstall Windows since (**I read about this a long time ago so may not be correct**) tied to the model of your mobo and/or hard drive.
Upgrading to a faster CPU or RAM shouldn't trigger a Windows reinstall. I remember upgrading from a AM2 Athlon 5200 dual core to AMD Phenom II X3 720BE processor using the same motherboard (ASUS M2A-VM) and I didn't have to reinstall OS. YMMV.
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