a cable is not plugged into the network?

I have a dell desktop, just over a year old, with Windows Vista.
It keeps saying "a cable is not plugged into the network adaptor". Or..."there might be a problem with one or more of the network adaptors"
or...."plug a cable into network adaptor for Local Area Connection"
It takes forever to view,send anything, as the computer works 10 seconds, then goes into this response, then comes back for a few seconds, etc.
I called Dell, had a new phone line put in, call my internet provider - Verizon(who wouldn't do a thing, but say it must be my computer)....so far, it still does this all day and night.
Help!!