If the router supports IPv6 you can find an IP address by pinging ff02::1. The exact command needed to ping that IP address depend on the OS you do it from, on Linux this command can be used ping6 -nc2 ff02::1%eth0
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If the router supports IPv4 you can find an IP address by scanning all the possible IP addresses. The 222 /8 prefixes it could possibly be using have in total 3724541952 IP addresses. If the connection between computer and router can run at 1Gbit/s, it can handle at least 83333 packets per second, at that speed you can scan all the IP addresses in less than 13 hours.
Some IP addresses are more likely than others. By trying the most likely IP addresses first, you'll probably find the correct one much faster. Ranges which makes sense to try first are private and link-local ranges 192.168.0.0/16, 172.16.0.0/12, 10.0.0.0/8, 100.64.0.0/10, 169.254.0.0/16.
For best performance you need to use a scanning tool, which only send one ARP request to each IP and look for an ARP reply.
If neither of those work, there should be some reset procedure, which will bring the router into a known configuration.
Does it have an inbuilt DHCP server that's running? i.e. if you connect to it's Wifi or Ethernet, do you get it serve you IP addresses? Can you tell us what the model name is? – LuckySpoon – 2015-01-06T03:33:03.977
It's a Belkin N+ F5D8236-4 – jason – 2015-01-06T03:53:35.460
don't know if it has an inbuilt dhcp server. when i connected it via ethernet to my laptop and ran ipconfig, my laptop showed an ipv4 address of 169.254.0.23 and a subnet mask of 255.255.0.0. these numbers seem very odd to me, as i use comcast so my gateway is normally 10.0.0.1 with 255.255.255.0 subnet mask. – jason – 2015-01-06T04:34:07.053
The 169.254.0.0/16 range is reserved for autoconfiguration; a machine that doesn't use DHCP or can't find DHCP will select an address in the region more or less randomly. Since your laptop picked an address in that range, the router isn't providing DHCP service to your laptop. You might try scanning that range with nmap, too, to see if the router autoconfigured itself. – Fred – 2015-01-06T05:00:19.113
running -sP 169.254.0.0/16 now – jason – 2015-01-06T05:11:18.680
ran -sP 169.254.0.0/16, said host is up for 169.254.92.173 and .176.107, but can't access the AP router through these IPs. will see what else shows as a host tomorrow when i wake up. thanks for the help so far. – jason – 2015-01-06T05:41:42.043
One more thing, if you are looking for a web interface, look for an open port 80 (http:) or 443 (https:).
nmap -p 80 169.254.0.0/16
for example. – Fred – 2015-01-06T15:22:03.130ran -sP 169.254.0.0/16 this morning, got 4 hosts (.92.173, .220.23, .235.4, .245.218) but none worked to access the AP router's web interface. trying to look for an open port now, as suggested – jason – 2015-01-06T16:41:42.977
nmap -p 80 169.254.0.0/16 showed the same 4 hosts as above, each with "80/tcp unknown http" (and still none of these 4 allow the web interface). trying port 443 now – jason – 2015-01-06T17:30:40.287