The batteries installed from the factory, at least on the SHO's, is a "Medium Duty" rated battery.
As such, & given all the electronics, these batteries are only lasting 2-3yrs at best.
So yes, swap that out A.S.A.P.
Most of us have been upgrading to the Motorcraft Max battery, which can be had at any of your local FMC dealerships, for between $115-$130.
As far as the crank goes, in relation to the push button feature, I personally really do not know.
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