No need for a network card as every motherboard made in the last, I don't know, seven years has an integrated 10/100 chip.
I'd recommend you look into socket 754. I'll get you started.
http://www.newegg.com/Product/Produc...82E16813135209
http://www.newegg.com/Product/Produc...82E16819104245
http://www.newegg.com/Product/Produc...82E16820161615
Throw in a microATX case, 80GB HDD, and 350 power supply and you've got a fast, cool and quiet, and reliable system for $200-$250 shipped. You can use her existing optical drive in addition to the peripherals. That's not including the operating system.
If you really wanted to cut corners, you could grab a 40GB, 300W PSU, and a 256MB stick of RAM, but you'd be saving $40 to $50 and the computer would be half as fast.
Alternatively, you could go take a peek at eBay or trading forums such as Anandtech. I'd imagine you could get a comparable used system for under $200 shipped.
Do you know if her case is ATX compatible? You could also use that, if it is.