Ha! In the spirit of helping others out, I will post the solution. After reading many more threads where RM was not connecting after updates, I have discovered the problem. In one thread, the poster said he clicked "Update Driver" in Device Manager on the Profiler icon, and that took care of his problem. When I looked, there was no driver, and when I clicked update, it said there were no drivers available?
So, I deleted RM (again), and it's associated files, turned off my antivirus, and reinstalled RM 3.2.72.....and it works! I have the latest OS, and RM working. The anti virus has been the main culprit over the last couple of years, blocking the driver from installing.