Trouble With Starting

Engine would not start (knocking sound - different than sound when battery low)
Knocking sound came from starter
Measured battery with own meter and was OK
Took battery to auto parts store who also said battery was "100%"
Measured charging system (alternator) with own meter and was OK
Replaced starter with one that was remanufactured
Engine started first time and several times subsequently
Let sit overnight and tried starting again in morning.  Brief pause when turning key before engine turned over (sounded like low power).  All lights at normal brightness; nothing seemed out-of-the-ordinary in terms of power.  Two subsequent attempts resulted in successful starts with less lag time.
Was thinking there could be a slow drain on battery.  Maybe remanufactured started has internal short?  Or during replacement the power lines somehow come in contact with heat shield thus draining battery (?).  Any thoughts?  Much appreciated!