Good, since there was nothing obviously wrong with the information posted.

You can try reconnecting the MODEM and laptop back to normal (and recycle power). Look at the output of the following command
sudo ethtool enp3s0

and post the results for
Speed:
Duplex:
Port: Twisted Pair
auto-negotiation:
MDI-X:
Link detected:

michaelk - My entire terminal output:

catadmin@CATLAP ~ $ sudo ethtool enp3s0
[sudo] password for catadmin:
Settings for enp3s0:
Supported ports: [ TP MII ]
Supported link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
Supported pause frame use: No
Supports auto-negotiation: Yes
Advertised link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
Advertised pause frame use: Symmetric Receive-only
Advertised auto-negotiation: Yes
Link partner advertised link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
Link partner advertised pause frame use: No
Link partner advertised auto-negotiation: Yes
Speed: 100Mb/s
Duplex: Full
Port: MII
PHYAD: 0
Transceiver: internal
Auto-negotiation: on
Supports Wake-on: pumbg
Wake-on: g
Current message level: 0x00000033 (51)
drv probe ifdown ifup
Link detected: yes
catadmin@CATLAP ~ $

I think one issue is you having to power off and on the modem. so can you post the contents to

/etc/network/interfaces

its likely NOT to have this line
allow-hotplug enp3s0

leaping ahead since you know how to do commands try this

the empty line is deliberate

then re-check the contents of that file

each line should have one setting

I will show mine, but I don't need hotplugging

# interfaces(5) file used by ifup(8) and ifdown(8)
auto lo
iface lo inet loopback

yours might become

# interfaces(5) file used by ifup(8) and ifdown(8)
auto lo
iface lo inet loopback

allow-hotplug enp3s0

2) in case its not obvious, your distro does not use eth0 but enp3s0

upon reboot, if no net can you repost output of

That looks good.

See if there is anything in the output of dmesg there could be something related to enp3s0

I can report a happy ending.

The router has 4 outbound ethernet ports. The one I used for my laptop doesn't provide a signal while the other 3 do. Things are back to normal.

Thank you to all who offered advice.

Always pays to check the basics (cabling/posts) first. Strange that you had a link light though, and ethtool is useful for reporting link status. Anyway, good to see the problem is now resolved.