I've been having a similarly (extremely) frustrating issue. I found this page helped me to resolve the problem. http://support.esri.com/en/knowledgebase/techarticles/detail/38493 1. I went into the file manager and looked for the ed.lock and sr. lock files. 2. Some went away when I closed ArcCatalog 3. More went away when I closed ArcMap. 4. When I reopened the map, all but one of the sr.lock files were gone, and suddenly things worked as they should (after hours of trying to move a simple point!). I could tell it worked, when I clicked on the point in the edit menu, and a thin black cross appeared over the dot, instead of just the cyan-colored selection.
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