I hate repeating myself.
It seems only to the Internet is very slow. if the Motherboard is failing would the LAN device be running slower on overything.
In a word, yes.
The above combined with "I had disables the on-board LAN on the BIOS and installed the spare network card that we have got and the computer did not go through the POST.
Is what made me say what I did above about this being a hardware (mobo) issue. Now, I don't have the computer on a bench in front of me so there's no way I can test to verify, but you could, and should, take it to a qualified technician at a reputable shop and have them look at the unit.
There could be something else wrong with the computer, but from what you've said, and from my 15+ years of experience in industry I can tell you, I suspect the motherboard and continued discussion at this point will yield nothing. You need to take it in to a shop.....period, end of story.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.