It's fixed, but it doesn't appear to be the cache. With my hosting support, we disabled W3 Total Cache and Sitelock and it didn't make a difference. Then we tried adding a new plugin--Use Google Libraries. This solved the problem. From what I understand, now I get the vast libraries of Google versus the java script from the WordPress Library (which maybe isn't as current/have as much in it--not my words). Something changed after my last update because it was all working before.
This solved the link button and feature images problem. The Facebook Like Box wasn't broken, but I thought it was because a photo was updated and not text. It only updates text!
So once again with all of your help, my site is back on track.
P.S. Dave the link above to the Admin Flush W3TC plugin gives a warning that it hasn't been updated in 2 years.