New batteries can be defective - that's why they have a warranty.
If it will start by jumping, it's probably one of a few things:
First, I would check the valve clearance - the valves will tighten up over time and need to have the clearance reset to prevent a drop in compression which leads to hard starting.
Second, if the difference is cranking speed is noticeable when jumping, it might just be a weak battery - was the new battery properly activated? An AGM battery should be filled with the supplied acid, let stand for 20 to 60 minutes before being connected to an automatic charger and charged at appx. 1.25 amps (depends on the battery AH rating - a 14 AH battery should not be charged above 1.4 amps and a 10 AH battery should not be charged above 1 amp). After charging, the battery should be allowed to stand for at least 1 hour and then the open circuit voltage checked (12.8 volts is nominal) before installation.
Third, if the starter motor gets hot quickly, then it's perhaps a bad starter motor. The starter motor should not be run more than 5 seconds at a time or more than 30 seconds total without letting cool for 30 minutes. If the starter motor has a high current draw, then it may need replaced. Connect an volt meter across the battery terminals - if the voltage drops below 10.5 volts when the starter motor is running, either the battery is weak or the starter motor needs replaced.
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