When I open the game, it takes a bit long to get to the main screen. And when I choose a mission to play, the game runs very slow. I can't fix the problem yet. And I'm sure the problem is not my Video card nor my ram memory because I can run with no problem, for example ProEvolution Soccer 2008. That ALSO MEANS MY DIRECTX 9.0c is ok as well.
I uninstalled COD2 and then reinstalled it and got the same problem and result again.
Maybe if I try installing the game with a new CD, well I'm not sure, though.

What are your PC specs? DX9 doesn't matter if you dont have the gfx card that actually supports it.

2100 MHTZ PROCESSOR INTEL PENTIUM IV
512 RAM MEMORY
NVIDIAGEFORCE 5500 graphic accelerator

If you mean the GeForce FX 5500, than thats your problem right there, thats a very old card now. No way is it capable of running COD2 except on the lowest of settings. Your CPU is slow for games and 512MB memory is only good for normal PC use not gaming. I'm afraid your whole PC is just not up to gaming.

yes, NVIDIAGEFORCE FX 5500. But, how come my computer can run PES 2008 with no problem?

Because that game doesnt need to push your PCs graphics hardware like COD2 does.

Does nvidiageforce fx 5500 equals a 256 mb graphics card? At least my pc says that

Yes the FX5500 has 256MB of video memory.

Maybe if I buy a 1 gb ram memory for my pc, COD2 will work well. What do you think?

A 1GB RAM upgrade would only make a minimum difference, RAM will only help your load times, you need a new gfx card.