If you do not have a networking background i'll try not to be technical. Here goes:
"what happens if I configure my own Ip address to be one that is allready registerd to someone else"
(let me ask you)What do you think will happen if you change your mailbox to read the same address as your neighbor? Do you think you will trick the mailman into placing mail in the wrong box? If your mailman has been delivering mail for over 5 years on the same route, you wont trick him, and computers have even better memories than people you won't trick them either.
Besides, just like the mailman only has 1 letter to deliver to only one of the boxes, network packets only travel in single segments, they won't split into 2 just because there are 2 addresses.(so either way only 1 computer would get the info)
"Why wouldent it work? What holds back my router from broadcasting this as my IP address?"
In order for your router to connect to any network segment it will always check and be checked to insure it does not carry duplicate info that may already exist on that segment.(i.e. duplicate addresses)
You could configure the router to hold the exact address info, but once it connects it will be rejected as a duplicate.
Hope this helps...