Is there a timeframe for this build? I've looked around at parts, and needing to buy both the os and monitor makes this near impossible. I have two possibilities I was able to come up with.
Option 1: Self built
Gigabyte 785g and athlon x2 240
$103
Wintec 2 gb ddr2 800
$44 plus shipping
Western Digital 640 AALS
$50 and out of stock at the moment, but it seems to come back into stock variably...if you refresh for maybe 15 minutes or so, it should come back in stock at some point and then order as fast as you can
Visiontek 4850 1gb memory
$117, but out of stock atm-you can look at other sites/manufacturers but they'll be around this price
NZXT midtower case
$30 AR
Corsair 400w
$40 AR plus shipping
21.5 inch monitor
$120
Windows 7 home 64 bit oem
$105
Optical drive:just find a cheap free shipping dvd burner
$30
Total=$639 plus shipping for some components
Option 2: buy prebuilt
Dell Inspiron 546 MT
$329
This is assuming the motherboard has a pci-16x slot available. If so, you can replace the stock powersupply (it probably won't be sufficient to power a dedicated gpu) and drop in a video card. You'll also have to buy a monitor. Using the prices for those components from option 1, that is...
Corsair 400w=$40 plus shipping
4850=$117
Monitor=$120
Total=$606 plus shipping
Keep your eye open for prebuilts, I'm sure a deal will come along that will be somewhat sufficient.
A few other options:
Is your nephew a student? If so, see about picking up a student copy of windows 7 for cheap. Look at
this thread for more info.
Second, can you put more money into this later? If you don't worry about buying the video card now, you can shave off $100 and possibly find a better deal in the future. That would put you much closer to your original budget. I understand that this is meant to be for games, but the 785g chipset should at least let you play old games decently.
Last, as others have suggested, look into buying components used. In addition to the anandtech for sale/trade forums, you can look at your local craigslist.
Good luck with this, it's a tough goal to reach.