I'm having a similar issue, fully charged Odesey battery, turn the key, dash lights up does gauge sweep, click the M switch, push starter button, I get one click, then the gauges reset but no start...... sounds like starter bendix partially engages, but no start .....
SO.....at that point, you need to have a voltmeter at the ready.....and leave the ignition switch ON and start checking voltages at the battery posts. Might need to watch the voltage as you try to start again.
Just because a battery is "fully charged" doesn't necessarily mean that it is healthy.....even if it is brand new.
You don't have the current capacity to run the starter, because of a battery that has gone bad and won't supply the necessary current OR you have a bad main battery cable end that is loose or corroded. Much less likely is a shorted solenoid or starter motor or liquid in a cylinder causing the engine to be locked up.