Try trace routing something, see the first ip that is displayed that should be your router. Im not too sure, just trial and error. For trace routing (lol), you dont have to download any programs or such.
Start => Run => Cmd => tracert www.google.com
Hit enter. Here is a sample of mine :
C:\Documents and Settings\NeoeN>tracert www.google.com
Tracing route to www.l.google.com [188.8.131.52]
over a maximum of 30 hops:
1 2 ms 1 ms 1 ms 192.168.1.1
2 * * * Request timed out.
3 85 ms 53 ms 56 ms dsl-KK-static-184.108.40.206.airtelbroadband.in
4 * * * Request timed out.
5 72 ms 43 ms 102 ms 220.127.116.11
6 57 ms 64 ms 49 ms 18.104.22.168
7 314 ms 299 ms 299 ms sl-gw39-nyc-11-3.sprintlink.net [22.214.171.124]
. . .
So the first number over there is my modem's ip.
Hope that helps.
Ehhh I think i just now understood your question. Any serial number printed on your router? Any name or anything? or is just 1 big black box.