HRX217HZA starter not working

Hello.  I got a new Honda mower with the electric start due to a broken collar bone and bad back.  The electric starter never did work well.  In fact, I'd have to engage everything for it to work (blade control, blade control button and drive clutch lever).  After a few months it doesn't work at all.  It cranks over and spins.  Just doesn't engage the engine for some reason.  It will start with one pull and will start with the electric start when it's warmed up.
 
Checked battery, 60%, charged it to 100% then took it into a Honda warranty service center to get it checked out.  They crank it over several intervals, nothing.  Pull start it, starts one pull (like I've had to do to get it started).  A week later, service center calls, 'we can't find anything wrong with it, it starts just fine'.  I get there, it won't start using electric start.  The guy pulls start it, say's 'see, it works fine'.  Shuts it off.  Then uses the electric start and it starts up.  I'm just flabbergasted at the guy at this point.  He proceeds to tell me the battery was dead and he has a trickle charger for $120.  Dude, I charged it before I dropped it off.  So caught him on that one.  Tried blaming it on my charger.  Charged me a $45 assessment fee.  
 
I'll take it to a different service center later on in the season.  It starts easy with the recoil and collar bone is all healed.  I'll put the next service center on notice about my first experience.  Definitely a warranty issue.
 
So to make a long story short, has anyone experienced this or know what it could be?  I paid for an electric starter and I would like it to work.  It should fire this thing up real quick.  Like a car.
 
Thanks for any help.