Battery or Adapter error?

Bought my son a HOMCOM Electric Go Kart 24V as a starter. It was in its original box for 3 months.

Today I opened it and tried to charge the battery as the manual wrote.

1. Adapter green led turned on

2. After plugged in the battery the green led turned off

3. Plugged out the adapter and tried to replug, green led was on for like 10 seconds (without battery), then died, multimeter shows 0.03V

4. Now the adapter is silent

How do I know if the battery killed the adapter, or both are dead because I'm unlucky?

And how the hell can I search for a charger / battery online? Because I find 24V5Ah without that T plug. Charger is another hell, I have 24V adapters but they are not chargers...GeminiAI said it might kill the adapter when it tries to pull too much voltage, and the adapter is fix 24V.