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Is it a new or used replacement battery!...use a DVM or multimeter across the battery terminals if you read 11 volts or less then the battery may be at fault if it reads 13.4v this indicates the battery is ok!
Next switch your headlights on with the ignition in the on position but don't start the engine. Is the lights bright if so the battery would appear to be good. A quick check for the alternator is to get the engine started apply the meter across the connected battery their should be a small rise in the voltage reading If using an analogue meter use correct polarity...The DVM uses an auto correct polarity irrespective of what lead is used.
The use of the use of charger across the battery may have just been enough to start the engine...the battery is my suspect.
6 minutes ago by Thomas