I like the direction that dizzy4 is suggestion, but there are some minor problems.
1. mini-ITX case, micro-ATX board. compatibility issue.
2. overpriced memory selection for 1333 speed stuff, either save on something cheaper or go with 1600 speed or better to alleviate GPU bottlenecks (not a critical issue for this build, but we're talking a few dollars so might as well get it right)
3. poor drive selection for the intended use of the machine. A 120/128GB SSD can be had for the same price and is typically more than enough space for an office use machine. Otherwise, there are faster, more modern drives available with higher platter density. The F3 was the bandwagon drive 2 years ago. Now it's old news.
Solve these issues, and you have yourself a pretty good direction to head.
Here's a build idea that pushes to the higher end of that budget, but will probably be with your friend for longer than his P4 system was.
CPU/GPU/MOBO:
http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.1102160
Another suggestion here for an AMD approach. I'm including a quad core Trinity recommendation on a motherboard that will be in it for the long haul with its heatsunk VRM package.
RAM:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231461
Use $5 off promo code. You can choose to run it however fast you want really. Bump the voltage to 1.5V and you can probably get a stable memory speed of 2000MT/s if you want. If you don't want to mess with it, just run it at a low voltage setting and stick to ~1600 speeds and you're set.
HD:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820249025
This 256GB SSD performs on par with the Sammy 830 and Crucial M4 drives. This is the best price and performance on an SSD this size you will find right now. I figure, this should be MORE THAN ENOUGH space for an office machine, with room to expand out into other tasks.
Optical:
http://www.newegg.com/Product/Product.aspx?Item=N82E16827106289
Actually, any decent DVD burner is fine, this one happens to have free shipping right now, enjoy.
Case:
http://www.newegg.com/Product/Product.aspx?Item=N82E16811352009
This is a really neat little case actually. Well made, good air-flow, reasonable size, professional looking. Supports 2.5" drive mounting (for the SSD) native.
PSU:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371033
A nice reliable PSU. If you wanted to alter the balance of the build in any way, I would suggest upgrading this to an 80+ gold unit, which would cost another $20 or so.
After shipping and an OEM copy of windows, figure about $590.
Edited by mdocod - 11/4/12 at 11:36pm