Thanks, but you missed an edit of mine in my OP.Brummelchen wrote:try this - close firefox, rename cert9.db/key4.db in cert9.old/key4.old (delete cert8.db/key3.db if present), restart fox. maybe cert store damaged.
After refreshing Firefox without fixing things, I uninstalled and then reinstalled Firefox. When that did not fix things, I copied a profile from 1 of the unaffected computers to that 1 with the issue and it, too, did not fix things. That should have replaced a corrupted cert store with a good one and yet things apparently were not corrected.