If you're gonna upgrade the CPU, you're gonna need to upgrade a motherboard that has the same sockets.
If you get a new motherboard, you're gonna need to buy new DDR3 chips RAM cause most likely your moms computer uses >DDR2 chips.
Might as well buy a new clean 7200rpm hard drive.
You should just build her a new computer...
You said you had a custom built 3k computer so I'm sure you'll understand.