If you suspect that the battery in your generator is dead, here are some steps you can take to test it:

Check the voltage: Use a multimeter to check the voltage of the battery. A fully charged battery should read around 12.6 volts. If the voltage is lower than 12 volts, the battery may be discharged.

Load test: A load test can determine if the battery can deliver the required amount of current to start the generator. To perform a load test, connect a load tester to the battery and measure the voltage while applying a load. If the voltage drops significantly while the load is applied, the battery may not be able to deliver the required current to start the generator.

Visual inspection: Inspect the battery for any signs of damage, corrosion or leakage. If the battery terminals are corroded, clean them with a wire brush and a solution of baking soda and water.

Check the electrolyte levels: If your battery is not a maintenance-free type, check the electrolyte levels and add distilled water as needed to bring the levels to the recommended level. A low electrolyte level can cause the battery to not function properly.

In summary, checking the battery voltage, performing a load test, visually inspecting the battery, and checking the electrolyte levels can help you determine if the battery in your generator is dead. If you find that the battery is indeed dead, it will need to be charged or replaced. It is recommended to consult your generator's manual or seek the help of a professional technician if you are unsure about how to perform these tests.