I tried other ethernet cables and the router still did not link to the modem.
LOGS:
64 1st day 00:04:45 DHCP INFO DHCPC DHCP Service unavailable, recv no OFFER
63 1st day 00:04:42 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 1
62 1st day 00:04:40 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 1
61 1st day 00:04:36 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
60 1st day 00:04:34 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
59 1st day 00:04:32 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
58 1st day 00:04:15 DHCP INFO DHCPS:Recv INFORM from D4:3D:7E:9B:76:84
57 1st day 00:03:16 DHCP INFO DHCPS:Recv INFORM from 00:19
1:39:CF:31
56 1st day 00:03:08 DHCP INFO DHCPS:Recv INFORM from D4:3D:7E:9B:76:84
55 1st day 00:02:52 DHCP INFO DHCPC DHCP Service unavailable, recv no OFFER
54 1st day 00:02:50 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 1
53 1st day 00:02:48 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 1
52 1st day 00:02:44 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
51 1st day 00:02:42 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
50 1st day 00:02:40 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
49 1st day 00:01:43 DHCP INFO DHCPS:Recv INFORM from 00:19
1:39:CF:31
48 1st day 00:01:42 DHCP INFO DHCPS:Recv INFORM from D4:3D:7E:9B:76:84
47 1st day 00:01:30 DHCP INFO DHCPC DHCP Service unavailable, recv no OFFER
46 1st day 00:01:28 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 1
45 1st day 00:01:26 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 1
44 1st day 00:01:22 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
43 1st day 00:01:20 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
42 1st day 00:01:18 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 0
41 1st day 00:00:39 DHCP INFO DHCPS:Recv INFORM from 00:19
1:39:CF:31
40 1st day 00:00:38 DHCP INFO DHCPS:Recv INFORM from D4:3D:7E:9B:76:84
39 1st day 00:00:38 DHCP INFO DHCPC DHCP Service unavailable, recv no OFFER
38 1st day 00:00:36 DHCP INFO DHCPC Send DISCOVER with request ip 0 and unicast flag 1
37 1st day 00:00:35 DHCP INFO DHCPS:Send ACK to 192.168.1.100
36 1st day 00:00:34 DHCP INFO DHCPS:Recv REQUEST from 00:19
1:39:CF:31
35 1st day 00:00:34 DHCP INFO DHCPS:Send ACK to 192.168.1.101
DIAGNOSTICS:
Pinging 192.168.1.1 with 64 bytes of data:
Reply from 192.168.1.1: bytes=64 time=1 TTL=64 seq=1
Reply from 192.168.1.1: bytes=64 time=1 TTL=64 seq=2
Reply from 192.168.1.1: bytes=64 time=1 TTL=64 seq=3
Reply from 192.168.1.1: bytes=64 time=1 TTL=64 seq=4
Ping statistics for 192.168.1.1
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss)
Approximate round trip times in milliseconds:
Minimum = 1, Maximum = 1, Average = 1