The solenoid clicks but,  the starter will not engage.  The piston is movable by hand.  What is typically the problem?  New starter motor needed?  Electrical connection?  60 HP ELPTO.

Sounds like a weak battery to me.   You may have charged it, but if its got a bad cell this will happen.

I'll give it a whirl.

Start with your battery, i.e. check the connections, charge, and load test it.  You'd be surprised how many electrical problems are due to a loose battery terminal connection (@ the battery or @ the engine), especially if you're using wingnuts on the terminals (swap those out!).

Merc manuals have a flow chart of tests to follow to diagnose this problem, all you need for most of the tests is a multimeter.

Thanks