Here's what i'm suggesting you should do:
Basically what you need to do is to get WinRoute Firewall, which can act as a DHCP server (to assign addresses), and authenticate any users and thus can set their access privleges.
The only thing that you'll need to remember is that by doing this, you will have to leave your box running Server on ALL the time, otherwise you wont be able to get network addresses or access the internet.
I'm not familiar with Linksys routers (I presume thats what it is, given your diagram), but if it has the option to set DHCP to be able to set 'gateway' it will need to be pointed at the IP address of the Server, as will DNS, if you can set them. If not, you'll have to disable DHCP on the router and set it up on the server.