It is still not even showing
Are you using a wifi adapter?
Dont know if anything here may be of help:
Note "solution" already marked as @Aravisian post #11.
It seemed marked since there was a partial solution, but not a complete one.
And this issue has me baffled, since the symptoms suggest that the linux-modules-extra package needed to be installed, as suggested in post 11.
Everything about it says kernel, I think. Part of the problem is due to Realteks unwillingness to show any support for Open source. It's like troubleshooting Nivdia.
If the OP was willing to go ahead and upgrade to Zorin OS 16 beta, I suspect the 5.8 kernel would have this covered. The only other option I can think of is that the OP install a newer (later) kernel on the current Zorin OS 15.3 build.
I read about bad kernel and good kernel affecting realtek 8169 (not 8168) and BIOS update helped.
Typically it helps to do a rmmod r8169 + modprobe r8169 to work around the BIOS bug.
Don't know about you, but I could not begin to fathom the differences between driver versions.
The ethernet cable goes directly into the motherboard, the wifi I have a wifi card (which has no ethernet port).
Yes partial solution this is probably separate issues that should have different threads. The marked solution fixed the wifi. The ethernet is still the issue.
Please clarify; is your wifi working or is your wifi working but only very slowly?
The wifi connects but the speed is inconsistant. it will be fast for 20 minutes then slow down for an hour. then fast again. resetting m computer seems to fix it usually
This guide covers multiple steps to recover wifi speed. As you scroll down, you may note a Bug in Debian based distros - which includes Ubuntu and Zorin.
Whether this bug affects you, is uncertain. But it gives a workaround for that in the guide.
Solution 6 listed in the guide is also a common solution and I can confirm does still work in Ubuntu 20.04.