Hello and welcome to Fixya.
Use a multimeter to measure the voltage from the connector that comes out from the adapter and make sure it matches or is very near the reported voltage in the bottom label of the adapter.
to test the ac adapter that its working and in good condition:
First If the adapter gives out DC 12-24Volt, then you could get a 24volt car lamp and wire it up to the connector coming out from the ac adapter. IF the light is steady then the power supply is good. If the adapter gives out more than 24volt I would not recommend testing it with a car lamp.
If the Light is not steady, flickers or dims out, then the power supply is bad and would need repairs or replacement, replacement being the easier option for you.