I think my costs for my system were:
Motherboard: Gigabyte socket 478 motherboard: $100
Processor: Pentium 4 2.4C 800mhz FSB (which overclocked easily to 3.2ghz): $175 i believe
Memory: OCZ dual channel 512mb PC3200: $80 (you can now get 1gb easily for that price or less)
Video card: ATI 9800XT: got lucky and was able to get it for $180 at the time
Case: $50?
Power Supply: $45 (which i upgraded after two 1/2 years)
So that came to around $630, since I already had a hard drive, my OS, and a CD drive at the time.
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Now, lets see what we can get at comparable prices today, eh?
Processor:
AMD Athlon 64 X2 3800+ AM2 processor -- overclock it: $150.00 newegg
Motherboard:
Gigabyte GA-M55SLI-S4 Socket AM2 -- has sli, great reviews: <$100 newegg -- if that is too much, you can find ones for even lower
Video Card:
Nvidia GeForce 7600GS PCI express -- take your pick of a good manufacturer: around $150 newegg
Memory:
CORSAIR XMS2 1GB (2 x 512MB) DDR2 800 (PC2 6400) -- dual channel too: <$100 newegg
So now we are up to $500.00. At this point, I'll leave you to decide on your case, power supply, sound card, hard drive, and other things you might need. Hopefully, you can make things easier on yourself by taking some components out of an older system (recommend AGAINST doing this with the power supply though, unless it is high in quality) and use accesories from older computers as well (keyboard, monitor, speakers, etc).
Yes, it does seem that you will be going over the $600.00 limit to build yourself a quality homebuilt system, but don't lose heart! Home built systems, in my opinion, trounce everyday manufacturers like Dell and HP in terms of quality parts and performance.