Alright, let's see what we can do:
(all parts come from newegg.com except for the memory, which comes from crucial.com)
Enlight 7237AZ 340W case (AMD approved) - $60
Epox 8KHA+ (Via KT266A chipset) motherboard - $105
AMD Athlon XP 1700+ OEM CPU - $137
GlobalWin WBK38 Heatsink and Fan - $19
256MB PC2100 DDR memory - $72
IBM 60GXP 40GB Hard Drive - $89
Pioneer 16X Tray-load DVD-ROM - $70
Teac Floppy Drive - $9
Hercules GeForce 2 Titanium video card - $118
Linksys 10/100 network card - $15
Keyboard, Mouse, and speakers - $25 (your estimate)
Shipping - $49.83
Total - $743.83
I did a kind of a generic setup here because you weren't too specific on what the system will be used for. Does your cousin want to play DVDs, play games, burn CDs, or all of the above? This setup will be a good DVD and gaming machine but doesn't include a CD burner. That would probably set you back another $70.
These are my recommendations, your mileage may vary.
Good Luck!
Nick