Hi Yumi,
You plan on recycling/re-using a LOT of old parts but haven't detailed what they are in order to provide assistance with what would be compatible with them.
Of major concern would be the graphics card, case and power supply. Without more detailed information on these components, there is no way to offer advice on upgrades that would be compatible with your older parts.
If you would consider simply re-using your old monitor, keyboard and mouse, you can indeed build a totally new system for under $800 that would play all the games you mentioned (and more) and be current and high-end on the performance scale.. provided you do not mind assembling the parts yourself (it's fairly straight forward.. and you'll learn a LOT in the process!).
Also, 3.73ghz seems a bit unrealistic as well as your cache/specs given current CPU's do not run this high of speed. Some 2.xghz Athlon's are coined "4400+" but they are not running anywhere near 3.7ghz. Cache statistics are more a case of "number-numbness", since again, cpu architecture vs. performance has a lot less to do with marketing bullet items as opposed to real world performance/output. Even the most powerful CPU you can buy today (the Intel Core 2 Extreme runs at 2.9ghz with multiple cpu cores) do not run anywhere near this high.
An example full system might be the following:
Antec Sonata case with 450W Power Supply - $89
http://www.newegg.com/Product/Product.asp?Item=N82E16811129155
Athlon 64 3800+ (2.4ghz) 2000mhz HT - $109
http://www.newegg.com/Product/Product.asp?Item=N82E16819103631
Abit KN9 SLI AM2 motherboard Nforce 570 chipset - $122.99
http://www.newegg.com/Product/Product.asp?Item=N82E16813127236
OCZ 1gig dual-channel DDR2-800 kit (2x512) - $109.99
http://www.newegg.com/Product/Product.asp?Item=N82E16820227082
Pioneer DVD-R/W Combo (Dual Layer) - $31.99
http://www.newegg.com/Product/Product.asp?Item=N82E16827129001
Seagate SATA 160GB drive - $58.99
http://www.newegg.com/Product/Product.asp?Item=N82E16822148149
Radeon X1800XT PCI-Express - $199.99
http://www.newegg.com/Product/Product.asp?Item=N82E16814102007
Total = $722.94
Add another $109 if you cannot re-use your existing Win XP license/serial.
That above system will play everything out there with ramped settings, higher resolution, and be way, way overkill for the games you've mentioned. Down the road, you can easily snap in a second gig (2x512) or even a dual-core X2 should the need ever arise.