2009 Mini Cooper S - "garage queen" but this last winter a mouse (we think, found sunflower seed hulls laying on the manifolds) apparently ate thru a wire. Battery (after manual charge) shows as fully charged, but get NO sound when start pushed on fob, no interior lights, just 'dead'. Had to open with manual key. Just no sign of electrical connection at all.

 

You need a VOM. Volt-Ohm meter or continuity tester. You start at the battery and work yourself out from there.

Also, when you say "it shows as fully charged", what are you using for that? You are testing the battery with load or just voltage with no load? Testing a car battery for voltage only with no load means nothing.