Will not start

I will monitor battery on alarm, and during and after start up. Your thinking even though the battery has the voltage, it may not be carrying the Amps behind it. Good thinking. Will let you know. No ammeter, idiot lights. Smart Charger does not indicate any battery prob ie. Open cell fault, etc. And since I've replaced the alternator, I believe I hear an increase in cranking power.

Checked - dead cold, 42 degrees outside - pre-start, both batteries (parallel +together, -together) read 12.4V. Started right up, with engine running both read 14.25V. Alarm sounded both still had 14.25V, til auto shut down, and both went back to 12.5V, Repeated, had same results