Half-life Platinum edition is still best in my opinion. There is also... SoF. Another one worth trying is an online one, but it isn't completly first person. BFH(Battle Field Heroes) Here is its wiki page. http://en.wikipedia.org/wiki/Battlefield_Heroes
Oh, I had no problem with it, even though my computer is old it still has really good stats.(I have a Asus motherboard and graphics card, both were top of the line like three years ago, but I have been lazy about updating it)
Yeah, UT 2004 is just great, even if I still prefer the first Unreal Tournament with the extra weapons.
It's the same game. It's playable even though there's no T&L Hardware. But the graphic will be bad. He can try Call of Duty, or maybe the first Half-Life.
Deus Ex. Definately worth a look, kind of similar to Mass Effect gameplay-wise (very different story-wise)
Serious Sam First Encounter or/and Second Encounter Painkiller Mind that those games are about going trigger happy and killing everything that moves (or not), you probably won't like them if you only play games like Call of Duty...
Just to clear everything up, Halo: CE will run on his system, now the graphics are going to suck, and the lil guy you are during online play and the campaign (spartans?) are all going to be gray, but it will still run.