Yes, your router needs to know its public (WAN) IP address, default gateway address, and DNS server addresses. Typically this information is provided to your router via DHCP on most DOCSIS cable modem networks. It's likely that something went wrong when your router tried to detect its connection type, so it didn't (or thinks it didn't) get a response from a DHCP server.
One common cause of this with DOCSIS cable modems is that many cable modems "latch onto" the first MAC address they see out their LAN Ethernet port, and refuse to talk to any other MAC address until they are rebooted. [In some extreme cases, cable modems can be programmed by the ISP to only talk to the one MAC address you registered with the ISP, and you could end up having to call the ISP to get them to reprogram your cable modem.] This often causes problems when you upgrade from one router to another without fully power-cycling the modem at the appropriate time; it stays latched onto the old router's MAC address and won't talk to the new router. This also causes problems if you for some reason have a hub or switch between the cable modem and the router, and other devices hooked up to that hub/switch, allowing the cable modem to see MAC address of other devices than your router; your cable modem may latch onto one of those other devices MAC addresses, and ignore your router.
So, make sure you have a single Ethernet cable coming out of your cable modem's LAN port and directly into your router's WAN port. Now set your router for DHCP and reboot it. Make sure it is fully rebooted and fully sync'd to the cable network, then power-cycle your cable modem. Note that some cable modems have built-in battery backups, especially if they provide voice telephone services, so removing the power cord may not be enough; you may need to pull out the backup battery. After your cable modem is fully rebooted, see if your router got a DHCP lease from the network.
If this still doesn't work, it's probably time to troubleshoot your Ethernet cable. Or check the settings on your cable modem to see how it's configured. If your cable modem is actually a more sophisticated "cable gateway", it might have the ability to have its NAT and DHCP services turned off, which can make your network setup more complicated.
And there's still a rare chance that you have a cable modem that's been ISP-programmed for the MAC address of the previous router you were using. In which case you'll have to call your ISP.
It's theoretically possible to have cable modem service where there's no DHCP server on the network and you're expected to manually enter static IP address (and gateway and DNS server) information into your router, but unless you're in a backwaters town with a mom-and-pop cable operator, I doubt that's the case.