Modem works, but not recognized by routers

2 issues here.

#1 if you set up your router with a particular modem and then swap out modems. There is a chance that it will not recognize the new modem because the router had been originally configured with a different modem.  2 fixes.

Fix #1  Step 1. unplug both the modem coaxial cable, ethernet, and power down the CM.

            Step 2. unplug the cable modem from the CM and disconnect power supply.

            Step 3. Plug everything back in and power-up the CM first.

            Step 4. Plug everything back in and power-up the router second

If Fix #1 doesn't work try Fix #2

Reconfigure the router from the very beginning. Reset it and begin the installation of the router process again like you did when it was brand new.  It should pick up your new CM at that point.

BUT before you do any of that I would recommend you switch to the NETGEAR CM600 since the CM700 has the dreaded Intel 6 PUMA chipset.  You're NETGEAR CM700 is on the avoid list linked below.

I recommend the NETGEAR CM600 as they use a Broadcom chipset.  I use the CM600 and can verify it is 100% okay as I have run several tests with PingPlotter Pro and there is not latency issue with it.

https://approvedmodemlist.com/intel-puma-6-modem-list-chipset-defects/ 

Intel Puma 6 Defect Explained
Intel’s Puma 6 chipset included in several cable modems is defective as it allows high spikes in network latency quite often (slow web page loading, for example). These severe network latency spikes interfere with online gaming, streaming video, or simply surfing the web. Network jitter (variable latency) also causes problems.

The Puma 6 modems suffer from both latency and jitter. Some firmware updates have only temporarily fixed the problem and it seems Intel has no real fix for the issue. Consequently, these bad internet connections landed cable modem maker ARRIS in trouble with a pending lawsuit filed in California.