Solution 1:

Since it is simply functioning as a WAP device now, short of reseting the WAP and using the default, it might not be all that easy.

Try going through your ARP cache (arp -a in windows, might be similar in linux) and see if the WAP has an entry. Just try each address on your local subnet that's listed.

Other than that, the WAP should be completely transparent so unless you're already communicating with its IP, its IP probably won't show up in network traffic.

Solution 2:

Unless you get get in in from your arp cache (try doing ping 192.168.0.255 first), the only way I know to find it is port scanning. Using something like nmap to scan your network - a WAP should be listening on port 80, and possibly something like telnet as well. Try nmap 192.168.0.1/24

Solution 3:

IPCONFIG /ALL (in a command line in Windows) will tell you under the heading Default Gateway. ifconfig under Linux will tell you, and also on Mac OS X (command line), and in the GUI: Network preferences, select wireless, advanced (right below) and TCP/IP tab, router entry.

Solution 4:

Default IP is 192.168.2.1 for a Belkin router, but can't you do a tracert to, say google.com and then find out which one is your router? (It should usually be the first hop.)

Or you could look in your browser's history...

Solution 5:

to accomplish this on a modern windows OS from the command line

netsh wlan show networks mode=bssid

find the network to which you are interested and connected, note the bssid and then run

arp -a

now find the bssid you discovered above in the new list of physical addresses, your access points internet address is listed on the same line.