A steady LED light generally indicates that the computer is on and the display is asleep.
Before you get inpatient and start taking out screws or trying to open it up, which is not an easy task on that model.
Reset the SMC, as per > Resetting the System Management Controller (SMC)
1. Shut down the computer.
2. Unplug the computer's power cord.
3. Wait fifteen seconds.
4. Attach the computer's power cord.
5. Wait five seconds, then press the power button to turn on the computer.
Then run the AHT, as per > Using Apple Hardware Test