Keeping my fingers crossed.
On computer 1, I followed the suggestion to Run IPConfig/Release, IPConfig/Renew. I have had no trouble all afternoon, reconnecting 20 or 30 times.
Computer 2 has not had any problems for two days. 3 wks ago we had a hard drive failure and had to replace it. Just 2 days ago, MS finally notified us and installed Service Pack 3. Since then, no problems. Is the a coincidence?
Many many thanks to all those helping to this point. I may now be back running internet normally.