Darlene,
After looking at one of the Vaux's vacuum machines which would not power on, I discovered there is an apparent broken wire within the power cord "plug" end. I replaced the plug with an off-the-shelf, 15A-rated plug and it powers on. I assume this vacuum machine is fixed, but Kristina will let me know otherwise. Cautiously optimistic. At some point soon, I intend to replace the entire cord with a replacement for $17 so the vacuum machine is safer and more robust.
I will look at the 2nd vacuum machine, which has issues, but will likely spend little time on it at this point.
Michael L