The model number should be on the top side or bottom of the modem/router. eg: rannorton specified that his modem brand is Speedstream & its model no. is 2500 If you can find the brand name, chances are the model number will be close by.
To test if you have a NAT modem visit this site & read what it says in the grey box:
http://www.u.arizona.edu/~trw/games/nat_or_not.php It will say whether you have a NAT modem or not. Easy eh!