L3p3rM355i4h - The system ribbon13 listed wouldn't need a video card. It has pretty decent onboard video that's slightly below a Radeon X300 video card. That's damned good for onboard video if you're not a hardcore gamer.
What size was her old HD? Circuit City and Best Buys has 120GB HD's for $50 after rebate this week which is pretty good. If you don't want to deal with rebates, you can get an 80GB HD from Newegg at about $60. If you need a case, Newegg is having a 99 cent shipping sale.
Add in the HD and it would run roughly $350-370.
Assuming she'll recycle her old case/psu (hopefully the psu is not too bad), floppy drive, optical drive, mouse & keyboard and monitor.