On many models of older Macs, ethernet is not hot-connectable. That is, if the computer does not detect a live device ("live device" = something, like a modem or another computer, signalling its desire to make a connection) as being connected during the startup process, the computer will disable the ethernet port. The so;ution is to make sure such a device is present, connected, turned on and warmed up before booting the Mac.
Very often the live-device requirement can be met easily by incorporating an intermediate device, such as an ethernet hub, switch, or router, in the connection scheme and leaving that on all the time.
There is also the probability that your machine requires the use of a crossover cable (instead of a straight-through or patch-type cable) if you are connecting it directly to another older Mac or to a device (such as an old modem or printer) which does not have an auto-detect port. This non-Apple article addresses that -
https://it.uoregon.edu/connect-macs