If your Cat5 network cable is in good shape (you did not torture it too much when running it along your walls right ?) then 30 feet is more than fine. You can normally connect with a Cat5 cable from up to 300+ feet (that's what the norm says). I have the same kind of setup cable-wise, I spent one whole evening gluing my network cable around the corners of my rooms to reach the server. Works like a charm.
Regarding changing IPs, you should probably configure your box to use a static IP on your internal network (192.168.xxx.xxx). Not much reason to use DHCP when you have like 3 computers... It is the default solution under Windows because it even works for dummies
but you can do better than that.
Once you replace DHCP by a static IP in the network configuration for your card the router will adapt. The real problem you may have is if you accept connections from outside your network, through your cable provider. Unless you have a fixed IP at your provider's you will need to setup a kind of dynamic DNS entry that you refresh everytime you connect to the big world outside. DynDNS is a solution, there are others like NO-IP. The refresh part is usually taken care of either by the router (my Linksys has this, but it is old and behaves stupid) or a daemon you run locally on one of your machines.