1: I've never seen a 24-port swith be a DHCP server. They just don't exist. I don't think eve the big Cisco 4000 6000 or 8000 seriese switches do DHCP.
2: You DO NOT need a Gigabit switch for a LAN party. These are games that are designed to play over the internet!
3: The boradband devices are routers with a built in switch. The funtionality of DHCP is a service running on the router, not a function of the switch.
I agree with what has been suggested by others. A boradband router or even a Linux box would be great to hand out DHCP. Heck, just have your game server do it. Even a XP or 2000 box can hand out DHCP if you enable ICS.