I disagree about the 790gx suggestion. While it is the undisputed onboard GPU champ, most 790gx boards run around $100-$120 USD. That's money wasted when considering what this person's mom is going to be using the computer for. I would suggest the 780g, as it is more than enough power for what she'll be doing.
On that note, she might even be better off with a g31 based mobo + a cheap intel CPU. I just built a system for my aunt and she was looking for exactly the same things that your mom's looking for. I ended up getting her the following:
AMD Athlon X2 4850e (low power draw, 45 watts) ~$70
Biostar 780g Motherboard ~$50
$2 gb DDR2 6400 RAM ~$15
Antec Earthwatts 430W PSU ~$20(sale price)
160gb HDD ~$40
DVD+RW ~$20
Antec Sonata case ~$70
Total ~$300
Not bad considering I tested Counter Strike Source on it and got playable (30-50FPS) on med/high settings. I doubt your mother would play graphics intensive games but it shows you that you don't have to spend a fortune to build a gaming rig, let alone one that doesn't play games.
I highly recommend this setup to anyone that needs to build their parents/older relatives a new computer as it is the most cost efficient/power efficient build that I could come up with and I did a TON, A TON of research.
Edit:
You might have trouble finding the suggested PSU at that price, a 380 earthwatt Antec can be had for $20 though and that's still more than enough. If you want more power for gaming/graphics design later down the road, I suggest a HD 4670 graphics card. If you want to go with Intel, I'd recommend the E5200 with a G31 based motherboard. Finally, the case I got is a bit of a luxury item(my aunt wanted it to be completely inaudible) so a cheaper case is probably the better way to go. None of the items I listed make any noise anyways...
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