It is highly unusual for the wired connection to be less reliable then your wireless connections.
From your other thread, you have logically narrowed down the variables.
And it does look like its your ethernet cable which is at fault. (they are very cheap e.g. at click here)
But your mention of IP addressing problems could be a contributory factor ~ although I would expect the wireless connections to be affected as well in that case.
Can you elaborate on those?
Are you setting the router to expect a dynamically assigned IP by your ISP? (most ISPs do that).
I must commend you on your clear thinking despite the pressure from teenagers' homework!