It's likely this won't solve your problem (because I'm no expert and came here tonight with a problem of my own) but hopefully it will help or at least point in a useful direction.
The working machine
Code:
Destination Gateway Genmask Flags MSS Window irtt Iface
0.0.0.0 192.168.1.1 0.0.0.0 UG 0 0 0 enp0s3
192.168.1.0 0.0.0.0 255.255.255.0 U 0 0 0 enp0s3
192.168.99.0 0.0.0.0 255.255.255.0 U 0 0 0 enp0s8
192.168.99.0 0.0.0.0 255.255.255.0 U 0 0 0 enp0s8
So you clearly have two "up" interfaces, enp0s3 and enp0s8. Why enp0s8 has two entries that are identical, I don't understand. Obviously doesn't hurt anything.
The second (nonworking) machine has a 169.254 destination in the routing table. An address in that subnet would be an autoconf address, usually a "guess" by the system at what it hopes will be an available, usable address. It implies the system detects a link at the physical and data link layers but isn't able to locate a DHCP server at the network layer. I'd be interested in the output of "ifconfig eth0" on that machine.
Code:
Destination Gateway Genmask Flags MSS Window irtt Iface
192.168.1.0 0.0.0.0 255.255.255.0 U 0 0 0 eth0
169.254.0.0 0.0.0.0 255.255.0.0 U 0 0 0 eth0
0.0.0.0 192.168.1.1 0.0.0.0 UG 0 0 0 eth0
That 169.254 just doesn't belong, unless the address you have on eth0 is a 169.254 address. I am not certain of the exact command but I believe something along the lines of "route del 169.254.0.0 eth0" or "route del 169.254.0.0" will remove it.
The line indicating a route to 0.0.0.0 indicates eth0 is the default interface and 192.168.1.1 is the default gateway, which is good, and the line indicating a route to 192.168.1.0 is good.
I'd try deleting that autoconf route and see where it gets you.
Also, I would like to suggest it would be easier to read the terminal output if you include "code" tags around it... that will keep tables like these lined up nicely so the parsing is much easier. Otherwise the numbers jumble up to tired sleep-deprived eyes and make it hard to see where one address ends and the next one starts
Good Luck... Let us know how you get on...
CJ