local area connection - invalid IP address

> [...] when I take the ethernet cable out of my laptop and plug it into
> my desktop running windows 10, I keep getting the same error, that is,
> "local area connection does not have a valid ip address". [...]

   Did you restart the modem when you swapped computers?

> [...] I have tried many solutions suggested on the internet [...]

   Think, for a moment, about how little useful information that
(non-)description conveys to the non-psychics in your audience.

   Did any of those "many solutions" involve employing a (NAT) router
with your modem, so that you could connect multiple client devices at
the same time?