Time Machine: "Enter Time Machine" menu command does not do anything
I just had the same issue in 10.11 El Capitan: "Enter Time Machine" did nothing, and nothing relevant showed in Console.app.

I relaunched Finder (Apple menu > Force Quit > scroll to Finder and choose Relaunch) and the issue was then resolved.

This surprised me, given that the relevant app is /Applications/Time Machine.app, not Finder.  But it seems likely that Finder is actually responsible for the Time Machine display of the historic files: if I "Enter Time Machine", then check with ps or Activity Monitor via remote log in, I see no Time Machine process.  So perhaps /Applications/Time Machine.app simply tells Finder to start the display, then exits.