I suggest:

Starcraft - either Brood War or Wings of Liberty, both are excellent multiplayer games.

Doom - the original, that is. Get a sourceport like ZDoom or Skulltag, download one of the recently released megawads, and have some cooperative fun. Hexen also makes a great coop game, since it involves a lot of adventuring and puzzle solving.

Minecraft - fun game, good way to waste some hours. Start a private server on your LAN and have at it.

EDIT: oops. Doom and Hexen are violent FPS games, so nevermind. But the other games are still good options.

How old is your brother anyway?