Ye hubs and switches
Hubs and switches transport any data from one Network Interface Card (NIC) to another NIC. It just uses the MAC adress (unique number of the NIC) to transport data from one to another.
Hub accept any signal and transport it to all the other ports.
Switches accept any signal and tries to learn which port needs that data. So after learning which signal goes to which port, them switches are a lot faster than hubs.
DHCP is regulated at the DHCP service (a resident program). That DHCP service resides either on a server (windows 2003 dhcp service) or some router (your linksys routers with a dhcp service). DHCP is a TCP/IP protocol schematic and has nothing to do with switches and/or hubs. It's on a different layer in the OSI model.
Enabling DHCP at a computer means it is going to search for a DHCP server. If it finds one, it asks for an ip adress according with the appropriate gateway and subnet mask. The ip adress it gets is defined in the DHCP pool. Usually you make the DHCP server itself say 192.168.1.254 and give out a DHCP pool of 192.168.1.10 to 192.168.1.100. This gives you 100-10 = 90 ip adresses to put out.
You can use other computers out of the DHCP pool. I.E. the ip's 192.168.1.1 - 9 for your servers, printers, ftp server, etc. You can also use 192.168.101 - 253 for that.
If there are more than 90 gamerpc's connecting you can also expand your DHCP pool to say 192.168.1.253 as well. This will give you 253-10 = 243 ip adress to put out.
Don't make the DHCP too big, but also not too small. If people try reconnecting, they will get a new DHCP adress. Also don't make the lease time of the adress too long. 2/3 hours is long enough. Rule of thumb = your clients x 2. So if you have 64 clients, make the dhcp pool 128.
For more info see http://en.wikipedia.org/wiki/Dynamic_Host_Configuration_Protocol
Now back to yer situation
Taken my last picture in account:
If you set up router 1, 4 and 2 as switches then they are just that : switches. They'll try to learn which data goes to where. They have no ip adresses since they are just switches. No matter how many switches you have, they will all act as a switch.
If you set up router 3 with DHCP service on the LAN ports, it will give out ip adresses to all computers. You will have ip adresses because of the DHCP service and for the rest all the LAN ports are just acting as a switch. Also activate the firewall on router 3. Dunno if you can setup a firewall between lan ports.
Note that you don't use the WAN port of router 3 in this scenario! You don't need any routing since there is no other network to route to.
Extra info (or: how the hell does the data go?)
Note how the data will transport:
If a gamerpc connected to router 1 wants to access a game server it will travel like this: gamerpc -> router 1 (=switch) -> router 4 (= switch) -> router 3 (= dhcp) -> gameserver
If a gamerpc connected to router 2 wants to access a game server it will travel like this: gamerpc -> router 2 (=switch) -> router 4 (= switch) -> router 3 (= dhcp) -> gameserver
If a gamerpc connected to router 1 wants to access a gamerpc to router 2 it will travel like this: gamerpc -> router 1 (=switch) -> router 4 (= switch) -> router 2 (= switch) -> gamerpc
If gamerpc's are connecting to each other, your gameserver isn't affected. This saves bandwith on your gameserver.
In this scenario you could also make router 4 a nice firewall. If some gamerpc at router 1 tries to attack someone (and router 4's firewall blocks it), he can only affect gamerpcs on the same router. The rest of your network is at peace.
If you connect a ftp server on the spare LAN port of router 4 you can give your clients (the gamerpc's) a nice ftp server and it still won't affect your gameservers bandwith
Rule #0: People will do things you don't want to. You cannot stop them.
You can't control the gamerpc's. People will install download tools. They will hunt down the network for open shares, ftp's and dc++ connections. Accept Murphy's Law and accept that all people who are connected to your network are instantaneously incredibly smart and incredibly stupid at the same time. They will try to mess up your network. Nothing is more annoying than lag on your network because some moron/einstein has hogged 800mbit bandwith for downloading porn on his neigbour's pc.
So make rules. Make people sign the rules and make sure you can kick them out if they don't follow. Make sure they can't reconnect as well. Have them leave the area with their computer. Make no exceptions. It's your network and you decide.