As mentioned in the comments, you should be testing out that battery to determine whether it can be charged.
Go get a cheap battery tender / battery charger, and a voltmeter / multimeter.
Meter the battery voltage (If it's a lead-acid / car battery it should be at 12.8V for a full charge, 10.8-11 volts is usually a 'no charge' / fully depleted charge, under 10.8V and you should suspect the battery has been damaged to some extent, but try charging anyway.
Connect the charger, leave it a good 12 hours and come back, disconnect the battery, wait 20 minutes (The voltage will temporarily be higher just because it was recently being charged, give it time to trickle back down) and meter it again. If you're not getting significant increase in voltage at all, the battery is gone. If the voltage has increased a bit but isn't quite to 10-12.8V, charge it for a while more and then check it again.
After this, if you get it to the appropriate voltage, try starting the vehicle with the battery.
If at this point it can't start the vehicle, very likely the battery is not able to produce the required current for that vehicle anymore (likely due to age of battery), time to replace battery.
You could also get a battery tester once the battery has been successfully charged and measure the output current it is able to do. I imagine you at least need 200-300CCA.
Seperate note - It's good that you bought one of those lithium jump starters. You should keep that, as well as a multi-meter, in your glove box of your car at all times. That kit can jump start your car very likely about 8-12 times (or more) on a full charge, and only needs to be charged up every 6 months, they're a great tool to have around in case you find yourself (or others, as it's simple to pull out of your glove box and walk over) with a dead battery.
The voltmeter is important because you should be able to check your battery voltage before jumpstarting your car.
If your battery voltage is fine and your car won't start, try jumpstarting it, if so, your battery can't output enough current when it's charged.
If your battery voltage is below 11-12V, just jumpstart it and assume it's due to low charge on the battery (Either sitting for a while or not getting enough charge from the system).