Ethernet has a self-assigned IP address and will not be able to connect to the Internet. 2018

it gets an ip from the dhcp service in the router

if it can't then after a timeout it just auto pick one in the default range

if that happen it would likely not have an internet connection

since you tried the power cycling then I would suggest you try another Ethernet cable

and maybe How to reset NVRAM or PRAM on your Mac - Apple Support

also if you don't have other devices connected by Ethernet then if you could test with another device it would rule out the issue was not the mac

I have had the same (I think) problem and it seems to occur in my case when the Mac wakes up after it has been in Sleep mode. However, it always connected fine to the network and internet after a power switch on.

What did solve the problem (as a work around) was to create an extra, new wireless network on the same router, as I found that it only affected my machine when connected to the WiFi network that I was using when I upgraded to High Sierra - I was setting up a new machine so only had one wireless network in the network settings list.

Once I connected to the new network, the loss of connection after waking from sleep went away and I have not lost my connection since, although I am still searching for a fix so I can revert to using my original network.

For what it is worth I would:

A) see if it is sleep related i.e. only happens after it wakes up

B) goes away after you connect to a differently named network.

I thought I had found the solution by deleting various plist files in the configuration folder as I found mention of that, but frustratingly it did not fix it. I also tried resetting the NVRAM and SMC but to no avail. It seems to be keeping some hidden settings somewhere that I cannot find...