With that budget i think you will want a decent AMD Athlon XP line computer with a decent NF2 mobo. Will you want to overclock? Or is this just going to be regular stock computer? You can save moey if you don't overclock, but your performance from the machine won't be as good.
AMD Athlon XP-Mobile Processor (Cheap, great at stock speeds, also #1 overclocker in the XP line if you decide to do that)
Abit/DFI/Asus Motherboard (overclocking)
Gigabyte/Soyo/ECS motherboard...almost anything motherboard (if you will not want to overclock)
OCZ/Corsair/PQI/Ultra Memory (overclocking)
Mushkin/Kingston/Centron (great stock performance, not really built for overclocking if you get value series)
Doom3 will require a very good graphics card, so you might not be able to afford that. However a 9800 Pro/5900XT card will run ~$170-$200 i believe, and will play Doom3 decently.
Any case will do, you will want at least a 300watt PSU of good quality though for guaranteed stability...don't skimp on the PSU, it's basically the backbone of the PC. A crap one can blow in a month and take out your entire computer if it's bad enough.
You can run on built-in sound for now if you have to, a $150 sound card isn't necessary, and you might be completeely happpy with built in sound.
That about covers the basics, CDROM,floppy,HD all depend on the left over money and what you think you need.
Hope that helps...
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Compaq Presario V5000 laptop