Check that you have not locked the tracks containing the objects see image - click the padlock to lock/unlock the track.
Also some objects eg titles have multiple parts/tracks and if there is no clear space, or required number of tracks free where you want to move them then they will not move.
Also check for multiple applications of 'group' eg if you group two object three times you have to un-group three times to get the single objects back. Think, if your mind work that way, of nested parentheses:
Is your problem limited to this project only? Perhaps the clip is somehow corrupted?
If the problem is evident for anything you add to the timelines I'd suggest a re-install of your program. There is usually an option to 'Repair' an installation rather than starting all over again.