Ok so you've narrowed it down. As an experiment why don't you put the ethernet card in another slot? Don't put anything in the slot it was in. Its fine if you have to temporarily remove something.

I tried the card in two different slots. Something in the card must be shorting out.
I am going to buy a new card and see if that fixes the problem.

Thanks.

I bought a new network card and installed it. The computer runs like new.

Thanks to all individuals that replied to my request for help.

No problem.