You could get a decent gaming computer, and I agree that you would be best off getting new parts. Here is my recomendation:
ASUS P5B-E LGA 775 Intel P965 Express ATX Intel Motherboard - $151
http://www.newegg.com/Product/Produc...82E16813131070
Intel Core 2 Duo E6400 Conroe 2.13GHz 2M shared L2 Cache LGA 775 Processor - $221
http://www.newegg.com/Product/Produc...82E16819115004
Patriot 1GB (2 x 512MB) 240-Pin DDR2 SDRAM DDR2 533 (PC2 4200) Dual Channel Kit Desktop Memory - $104
http://www.newegg.com/Product/Produc...82E16820220068
Western Digital Caviar 160GB 7200 RPM 16MB Cache SATA 3.0Gb/s Hard Drive - $63
http://www.newegg.com/Product/Produc...82E16822136062
NEC Black CD/DVD±R/RW/RAM 2M Cache E-IDE / ATAPI DVD Burner - $30
http://www.newegg.com/Product/Produc...82E16827152076
XFX GeForce 7900GS 256MB 256-bit GDDR3 PCI Express x16 Video Card - $210
http://www.newegg.com/Product/Produc...82E16814150209
Antec True Power Trio ATX12V 650W Power Supply with Three 12V Rails - $130
http://www.newegg.com/Product/Produc...82E16817371001
The total here without a case is about $909. I verified that the RAM will be compatible with the motherboard I listed.
My Favorite Cases:
Thermaltake Armor jr Silver Chassis Aluminum ATX Mid Tower Computer Case - $129
http://www.newegg.com/Product/Produc...82E16811133016
Antec Nine Hundred Black Steel ATX Mid Tower Computer Case - $130
http://www.newegg.com/Product/Produc...82E16811129021
Antec Performance One P180B Black ATX Mid Tower Computer Case - $130
http://www.newegg.com/Product/Produc...82E16811129017
These cases will give you excellent airflow to keep your components cool.