10.x.y.z is an Internal IP addres and does not have an External DNS System to handle it. YOu need to setup your DNS Server as the Primary place where web requests will go when your PC Connects to the Net.
You add an entry onto the DNS table for BOTH the forward and the REverse Lookups, However be aware of the gotchya of the reverse numbersing scheme for IP Addressess .
Eg
PRIMARY LOOKUP TABLE
DNS-NAME ==> IP_ADDRESS
my.server.department.bighwig.com ==> 10.x.y.z
REVERSE LOOKUP TABLE
IP_ADDRESS ==> DNS Name
in-adder.z.y.x.10 ==> my.server.bighwig.com
DEPENDING ON THE SERVER YOU Configure DNS on, yu will gneed to get the Assignmant of the DNS Name from your Upstreamm provider , and REGISTER for External DNS Name space if you wish to have your IP Address accessable from the outside internet.
YOU did not specify WHAT is the Machine you are configuring your web server on, from your description this is behind a firewall, and you have your machine configured as a Static IP. This is only part of the equation, now you have to configure the rest of your routers to oint to your machine when they see bits that match your IP to go through your router.
See the O'Reiley book on DNS and BIND