Wow... where do I begin...
DHCP works by assigning an IP Address when the computer requests it. That "lease" is provided for a set period of time, based on what the DHCP server is configured for. Typically, that time frame ranges from 8 hours to 1 week. Now, when the IP Address is handed out, it's "reserved" for that period of time. HALF-WAY through the lease, the computer will contact the DHCP server again and request it keep the address. That means that if you have a DHCP server with a 1 week lease duration, every 3.5 days the computers attempt to renew the lease. Further, if the computer cannot renew it at the half way mark, it keeps the address originally given and periodically tries to renew it. So with a week long lease term, all computers can go a MINIMUM of 3.5 days without ANY DHCP server on the network at all before they start experiencing problems - PROVIDED no one turns them off or attempts to release and renew the lease.
Now, what version of Windows Server 2003 did you buy? Standard? Small Business Server? What? There's actually a HUGE difference in how you (may) have to do things. Of course, this site doesn't allow us to easily converse so a) you may never see this question, or b) I may never know if you reply to it. I would STRONGLY encourage you that for serious questions (like how to install a server) you should visit other sites and ask this question - even newsgroups - where two way communication is actually encouraged. I frequent two sites - you might try one or both (the latter does offer a free trial but it can be a pain to find) - www.tek-tips.com and www.experts-exchange.com
Now that said, if it's SBS (Small Business Server 2003), then you MUST do things as it wants you to, including disabling the router's DHCP server. SBS is designed to be VERY easy to manage and setup - BUT that ease requires a rigid method of setup and configuration. Further, aspects of it will fail and the server may start rebooting itself if you don't set it up properly.
If it's plain old server, then you spent more than you have to (SBS is cheaper) and it's not as easy to manage though it is more flexible (nothing should cause it to sporadically start rebooting itself unless there's a problem with the hardware.
With regards to the DSL, you should keep the router. DSL modem should plug into the router, the router should connect to the Gigabit switch, and all the other computers - and the server - should connect to the gigabit switch. Otherwise, you would need to buy another network adapter for the server. Then the server COULD act as the router.