Here are several ways to determine if you LabQuest power adapter is functioning.

1) Check to see that the LabQuest battery icon shows that the battery is charging.
It can take up to a minute for the battery icon to refresh.
Disconnecting and reconnecting a working adapter can force the icon to update faster.
What does the battery icon on my original LabQuest mean?
What does the battery icon on my LabQuest 2 mean?
What does the battery icon on my LabQuest 3 mean?

2) Use a multimeter or voltage probe to measure the voltage output of the adapter. It should measure around 5 V DC.
The LabQuest power supply is center-positive and outside negative.

3) Remove the battery from a working LabQuest that is turned off. Connect the AC adapter to the unit without the battery.
The unit should boot normally without the battery.

If you find you have a bad adapter, it will need to be replaced.
LabQuest^® Power Supply (LQ3-PS)