That old PC is useless. Your going to have to completely make a new PC.
Before you start being bombared with ideas, I strongly advise you go out and do some research. You have to decide :
1. Your budget
2. Intel or AMD
3. LGA775 (new intel socket) or Socket 478 (old intel socket), OR 939 (new amd socket) or 754 (old amd socket). Obviously, the old sockets are cheaper.
4. Using your budget, decide on a processor which will fit into your socket
5. Decide whether you want AGP (older) or PCI-E (newer)
6. Then decide on a motherboard
7. With the budget left:
Choose a graphics card on your selected platform
RAM (DDR or DDR2 depending on Intel or AMD)
Choose a hard drive IDE (older, cheaper), SATA (newer), SATA 2 (only on the latest motherboards)
Sound card (X-Fi is latest and most expensive) - Most motherboards have pretty decent on board sound though
Choose a case (good cooling, don't just go for looks)
Disk drive (CD or DVD, etc)
Floppy (comes in handy sometimes)
In that order is usually best
8. Finally, with the final money left :
Then you can post the spec up if you need/want to. Do enough research, and be sure that components are best. You want to be able to make your own judgement, and decide whether it suits your needs.
You will need at least a 9600 Pro on ATi, or a 6600 on nVidia to play Counterstrike Source.
A GB of RAM would also be best for it, and an average speed processor.