The router doesn't have a burned in address, it has a default address. This is so you can get at the configuration page with your web browser, or telnet. You then change it to whatever you want to use on your own network. You need to change your computer to an address in that subnet range to access the router. If the router uses a web interface, you go to your browser and put the routers default address in and you will get a configuration page. You then change the default address to work on your network.
For example, if the burned is 192.168.0.1, you could set up your PC to 192.168.0.10. The reboot everything, including switches. This is because your switches have tables that contain IP and MAC (not to be confused with Macintosh) addresses. If you change your IP address, your MAC address can still be cached in the switch and could prevent you from access the router.
When the configuration page comes up, you change the LAN address to an address in your subnet. If your subnet is 192.168.100.0, a standard address for a router is 192.168.100.1. If you have a router and a firewall and 192.168.100.1 is already taken, you could use 192.168.100.2. This address will be your default gateway on all your PCs. You then make any other changes that need to be made at this point. You then put your PCs address to an address on your subnet (192.168.100.20 for example - and don't forget to put the 192.168.100.1 in the gateway field). Reboot everything and you should be up and running.
The router can't have a burned-in IP address.. the IP address is modifiable. If you're wondering how the MAC address can be unique for all interface cards, thats because each vendor recieves a unique prefix from a governing body and then they assign unique serial numbers to each card they make.
Thus all MAC addresses worldwide should be unique... theoretically at least.