I want to set up a 'private' DHCP for serving internet within another network. I am inside a college network with a HTTP proxy being the only way out into the internet. The idea is to setup a DHCP server within this network that would connect directly to a ssh tunnel running on the server so that computers on the network could setup their connection to connect through my server instead of through the college's.

EG: Computer -> Server -> Tunnel Through Proxy -> Home Computer -> Internet.

I understand that there are many better ways for achieving this end goal for most machines, (I already have the ssh tunnel so my computers are already setup) but a Xbox 360 does not allow for any type of proxy settings that would be needed to route it normally through the tunneling server.

I have done some research into this, but nothing that really applies to what I want to set up. It seems that setting up two DHCP servers within a network can cause problems, and if that is the case this isn't an option, but I want to know for sure. And I don't really know what setup is unnecessary, do I need a DNS server too? I have played around with some software, but nothing has really stuck out yet.

My server computer is running Tiny Core Linux, headless with ssh.

It sounds like you're a little unclear about the role of DHCP here. DHCP wouldn't relate to any of your solution at all. You right that you wouldn't run two DHCP servers in a single subnet (not network mind, just a single L2 zone) but allocating your own addresses shouldn't bare any relation to making machines use a proxy. Xbox360 appears to support an http proxy just fine, so I dont see quite what the issue is there either.

Also note... We are not here to help you circumvent security mechanisms at your college / work place. You agree to follow their rules when you use it, and we will not promote ways of getting around them.

The Xbox 360 supports an HTTP proxy? That is a new one to me. And from your answer I see that I am obviously barking up the wrong tree with DHCP.

Sounds more like you want to set up your Linux machine as a gateway Router with NAT.

Yes, but a gateway to a ssh tunnel. Is this possible? What software would I need?

EDIT: After some research it looks like I would need another network card to do this. Which is something I would do. So my main question is can I use the same network for both cards (the one accepting the connections and the one sending them through the tunnel.

Yes if they are bridged, you'd handle traffic flow with iptables and possibly iproute2