I used to own a vanilla 6800 128mb card, I could run CS:S/HL2 at 1680x1050 with decent AA+AF, but I had a few things set lower, ran really well. COD2 should work at that resolution with a 7800gs but I can't gurantee it. BF2, unsure...
The rest of your system specs will be quite important to some of those games, like the amount of ram and processor you have, primarily.
HL2/CS:S definately, the others... you may need to run it without any AA and possibly reduced settings.
I will give you a tip.
Look for a 7800gs with the g71 chip. This one can be overclocked much better then the g70. Overclocking the 7800gs is very important to get the best performance out of it.
With a good CPU you are going to be GPU limited, so every extra mhz helps.
I run an opteron 170 system with a g70 7800gs. I have done a volt mod, and I can reach 500/1500... and that is really good for the g70, however the g71 version can go farther then this without any modding. With modding it can reach insane speeds... 600+ on the core.
Anyway, since you have an LCD, I would get the x1950pro AGP... you need all the power you can get since you have a set native resolution.
i used to own that card. Shit, I used to own alot of cards hehe! Anyway, that card will run COD2 but with the setting down a bit. This was on an AMD@2.4 system. In fact, i remember using dx7 so i could having everything set to high. It looked nice too!
Now CSS and valve games run great using that card.